Introduction and framework
As the citations provided with this question show, the argument Dennett makes is one that is widely made, with dozens of philosophers and scientists who believe in the illusory nature of free will advocating for suppressing this view. This is a very actively held position within philosophy, and I applaud asking this community to address how it can be evaluated.
The argument FOR suppression is made in two parts:
Belief in determinism over free will vitiates the agency of many people who accept determinism is true, and this is highly detrimental to the subsequent behavior of the new believer, as it reduces their psychological behavior of exercising will to overcome temptations, or to better themselves. IE achieving better outcomes in life is often the result of psychological effort, and belief in determinism reduces the exercise of that effort.
The psychological and sociological benefits of voluntary suppression of this knowledge (the supposed truth of determinism) are greater than the harms caused by a program of deception. The arguments for 2) are generally only made in a consequentialist framework, either utilitarian or Darwinian, as 2) is difficult to justify in the competing deontological/rights or Virtues formulations of moral thinking.
The counter argument is vigorously made by James Miles, who provides a large suite of argumentation paths -- many of which are efforts to rebut the claims in 1 and 2, but he also presents a specific positive argument against suppression. To summarize, he basically argues that:
Determinism has been shown to be true primarily by logical reasoning, more so that the scientific justification assumed by the illusionists. Miles supplements 3) with claims that belief in free will is irrational and "mystic", but these arguments are pretty clearly fallacious argument by name-calling.
TRUTH is a moral virtue in itself, and suppressing it is immoral (this is a Virtues ethic argument, and is supported by some deontological reasoning). A similar argument to 4) is made in the two Public Health essays -- but they argue this point under rights ethic (patient always has right to information), or consequentialism (harm from lack of trust in authorities if a deception is discovered exceeds any benefit from concealment of possibly misusable information).
There is significant sociological harm from the belief in free will, as it decreases both empathy and the efforts to achieve equality in our societies, and makes people more punitive in their interactions and policy choices.
OK -- trying to evaluate these arguments:
The evidence FOR 1) is fairly overwhelming. The understanding that determinism vitiates agency is widely understood from personal experience, with most advocates of free will noting this is a major cause of their rejection of determinism. Multiple determinists as well, including all the "illusionist" advocates for suppression, *AGREE with is point. Many determinists admit they find they must live their lives as if they have free will, as they find it impossible to practice agency otherwise. This is basically what all the suppressions cited are saying. There is anecdotal cultural evidence -- many Arabists cite the widespread Islamic belief in determinism, as a driver of the reduced technologic and economic growth in the muslim vs non-muslim worlds. And academic studies cited here have found this effect of reduced agency and morality in multiple studies.
Miles attempts to rebut this evidence, not by arguing against either the sociology or the psychology, but by making a logic argument -- that reduced agency is not a NECESSARY outcome of belief in determinism, and he cites the Stoics, who pursued pragmatic self improvements despite their deterministic beliefs as a counter example. However, there are ALWAYS logically possible alternatives to actual sociological and psychological effects. Sociology and psychology study not logical possibilities, but instead the actual effects among us humans. This part of Miles "rebuttal" is irrelevant in its point.
Aside on the Stoics -- Stoicism maximizes rational pragmatism, and applies determinism in a compatibilist way to reasoning. But, as with Miles first argument, most determinist thinking today is reductionist. And neither the value of reasoning any consequences due to it, nor any moral values, can be readily justified in a reductionist POV. Both reasoning, and moral argumentation and justification, are IRRELEVANT if our behavior is determined by biology, or the randomness of quantum mechanics. Miles suggested alternative, is not even available to him.
He also claimed that the empirical studies were methodological flawed, as they studied fatalism, not determinism. This claim is factually untrue, as claims of the reality of fatalism was not presented to the test subjects, just claims as to the reality of determinism. The inference from determinism to fatalism by the test subjects was made solely by them. IE -- this inference and coupling is part of human psychology and sociology, and Miles is himself engaged in "irrational" truth-denying about this.
So -- point 1) is well supported and I will proceed assuming it is true.
Note, I cite a meta-analysis in a discussion of point 2 that reaches the opposite conclusion, that point 1 is an artifact of small sample size experiments. This analysis is a strong argument against point 1, as meta-analyses trump individual study conclusions, but is an anomaly in the literature and is still in pre-publication peer review. As meta-analyses conclusions are highly influenceable by methodology, it is too early to reject point 1 based on this one.
Point 2a, the DEGREE of harm from belief in determinism, has not been articulated as well by the advocates of point 1. It is fairly apparent that the degree of harm from 1) COULD be catastrophic. If all agency is vitiated from us humans, our lives and society will collapse. BUT -- the widespread adoption of suppression as a program of action by the illusionists -- AND their demonstrated accomplishments in both philosophy and science despite their belief that determinism is true, and is catastrophic for agency -- is itself is a significant refuting test case for the catastrophic claim. These philosophic and scientific leading lights have managed to continue their productive lives despite their INTELLECTUAL acceptance of determinism, by living in a state of cognitive dissonance. Their presumption that the rest of humanity is incapable of this cognitive dissonance of continuing productive lives despite holding a viewpoint that should vitiate their agency if fully embraced -- is entirely unsupported.
instead, the evidence is that we humans are able to engage in cognitive dissonance, to assist our coping with the world. See this study on self deception among amateur swimmers: https://psych.colgate.edu/~ckeating/KEATING%20ARTICLES,%20CHAPTERS/Self-Deception%20&%20Competition%20Starek%20&%20Keating%201991.pdf The more successful swimmers most likely "knew" they were not the best, yet convinced themselves to say and think so anyway. Over-optimistic thinking was highly beneficial.
Similarly, we humans tend to underestimate difficult tasks even when we are familiar with them by approximately 3x. We also gravitate to the "sunk cost fallacy" of continuing a started task, even when it proves more difficult. This combination of optimism about project difficulty, plus stick-tuitiveness when project difficulty becomes undeniable, is a set of fallacies and self-deceptions which can reasonably be inferred have contributed massively to the growth of human infrastructure over the millennia. Selective self deception can have significant societal benefits.
In addition to the "catastrophic" claim appearing to contradict our human tendency to respond with cognitive dissonance when we have rational views that could harm us, the "catastrophic" claim is also not well supported by the experimental evidence. Despite the case for harm being strong, the case for SEVERE harm is not. The experiments cited show MARGINAL effects on the test subjects' behavior, not the catastrophic ones. And human psychology is adaptive, such that the marginal detriment seen in those studies could plausibly be counteracted by a better constructed cognitive dissonance response over time, such as the suppresionists seem to have constructed for themselves.
One meta study supports this case for skepticism about the ability of reasoned arguments to change human belief about free will, or our agency. This study found that the manipulation was effective, but that the effects of manipulation of free will beliefs are highly dependent on sample size in the studies, and correcting for small sample size errors eliminates any statistical significance. Also no long-term effects from the attempts to manipulate the beliefs of participants in the studies are apparent. https://psyarxiv.com/quwgr/ Note this meta analysis is still in pre publication review.
Additionally, the Arabists rationale for the detrimental effects of determinism in Muslim society, is a leap to a conclusion. Historically, the Islamic civilization has been a co-equal competitor to Christian, Hindu, and Confucian cultures. Its current relative disadvantage should therefore be traced to some more current cause, not one that has existed for more centuries than this current disadvantage has.
The instances of cognitive dissonance and self-deception undercut the argument for 2A, but make the argument for 2B, that the harms from a truth suppression are smaller than 2a, at least somewhat plausible. As does the complete lack of any blow-back from 2 decades of advocacy for suppression. However, that advocacy has so far been fairly ineffective, as there remain multiple public advocates asserting the "proof" of determinism.
An effective suppression of this supposed proof of determinism, most plausibly therefore would require a much more effective and coordinated effort, an ORGANIZATIONAL conspiracy, either by governments or some institutional body that controls publications in academic literature. The two public health citations in the Question's references, both cite a history of distrust of governments and of doctors that prior efforts to suppress information have created. A conspiracy to suppress this "information", which would have to be organized across multiple institutions, would reasonably be expected to not remain secret. And distrust of institutions is a fairly clear and current hazard in our societies today, with the populist anti-expertise movement sweeping ignorant semi-fascists to increased power in multiple democracies.
The 2B argument that the harm from secrecy is small, is therefore not well supported.
This discussion is not definitive, but the combined argument of 2, that the harm from belief in determinism exceeds that from a conspiracy to suppress this 'fact" is not well supported, and there are strong hints that both sides of that calculation may be in error. And as noted earlier, this is a solely CONSEQUENTIALIST argument, which does not stand up under virtue or rights/deontological ethics. With only one of three primary moral stances even plausibly supporting 2, and with even the consequentialist case weak if it is even positive at all, the second point of the suppression argument does not appear to be strong at all.
Looking at the counter argument now, for point 3, Miles makes two arguments. The first, 3a) is a reductionist one, that all behavior must be caused by biology, or random effects derived from quantum effects, and neither support free will. His second, 3B) is that agency requires selecting one's own values, and this can never be done because any justification of willing must be either uncaused or resort to an infinite regression of causes.
Both of these arguments suffer from an unstated assumption of One True Logic, which is not accepted today by the majority of logicians: https://www.cambridge.org/core/journals/think/article/abs/guide-to-logical-pluralism-for-nonlogicians/EDFDFA1C9EB65DB71848DABD6B12D877. If there are multiple logics, then neither of these "logic" arguments are compelling, as there is no necessity for any aspect of our world to abide by the logic that Miles assumes.
The first of them, 3a, also falls afoul of the rejection of reductionism within philosophy of science, in favor of emergence and pluralism see section 5 of https://plato.stanford.edu/entries/scientific-reduction/. Emergent phenomena are some other category, neither explicitly caused, nor random. Hence Miles asserts a false dichotomy, even within the logic he presumes. Emergence is still not a well characterized process, so we can't really spell out what this third option behaves like, but there is wide consensus that our world has emergent phenomenon none the less.
3b is just an application of Munchausen's Trilemma to the justification sequence of agent choice. That one of the legs of the Trilemma has logic problems (again, per the assumed One True Logic), does NOT mean that one of the other legs must be the case! Instead, all legs of the Trlemma have problems per classical logic -- the Trilemma is one of the demonstration cases that the classical logic it is based upon, DOES NOT APPLY (at least not fully) TO OUR WORLD. A trilemma based exclusion argument -- is intrinsically flawed.
Other arguments for 3 were evaluated by Chisea in https://digitalcommons.pace.edu/cgi/viewcontent.cgi?article=1850&context=lawfaculty, with the conclusion that arguments for and against free will and determinism are in a dialectic stalemate:
As a result, it seems that the free will problem has the argumentative structure John Martin Fischer called a “dialectical stalemate.”
So -- 3) is not a valid claim.
For point 4), all of the justifications summarized appear to be true, within their moral systems. BUT -- that is not a definitive case. Morality is noteworthy by having multiple competing frameworks, AND the possibility of reaching multiple different conclusions within a specific framework. With competing plausible frameworks, one needs to show that a selected framework is the most appropriate to apply that that specific moral problem. And most people judge taht -- when discussing possible collapse of our civilization (see the catastrophic argument in 2 above) consequentialist arguments, and in particular Darwinian consequentialist arguments, are generally the right kind of framework to weight most heavily. Rights and virtues, are most useful in cases where consequences are not catastrophic. 4 may be true, but it is trumped by 2, IF 2 were true. Because 2 seems more likely than not, NOT to be true, 4 has some weight.
Point 5) should be broken up into a point 5a), that belief in free will has effects of increasing support for a certain set of anti-equality and punitive morally harmful attitudes and behaviors, and a 5b) that the morally harmful claims in 1 can be ignored (or at least are dwarfed by 5a). %a, as with 1) appears to be well supported by multiple academic studies. It appears to be true TODAY. The effect size is again small however.
An interesting caveat, is that in the US and the UK at least, the neuroscience claims are increasing the belief in determinism in both societies, while simultaneously, the support for rehabilitation over punishment is decreasing, along with interest in societal equality. The social trends in both countries are the reverse of what is claimed in point 5. It is reasonable to infer that belief in free will was larger in the 1960-80 period, as determinist behaviorism had lost its control of academia, and neuroscientific determinism had not arisen as a movement. But this era was a high water point for equalization and rehabilitative policies, and electoral support for both. It is plausible to infer that belief in freedom of will, and determinism, even if they may have some small effect on rehabilitation and social equality, that effect is being swamped by some more consequential societal changes. This would be consistent with the "cognitive dissonance" critique of possible societal effects noted in 2.
Note also, as with the harm effects in 1, the meta-analysis in peer review did not support point 5a, and the effects in 5a were even more strongly discounted than those in 1.
For 5b, the arguments against point 1 by Miles were previously discussed and shown to be invalid. As the consequences of 1 are potentially of much greater magnitude than those of 5a on society, the assumption of 5b, to ignore more severe societal harms, while focusing on less severe ones, and 1 is better supported by experimental literature than 5a, the supporting rationale for 5b appears to be almost entirely lacking.
The case for suppression of determinism is weak, or less charitably, it fails entirely, as the support for point 2 is lacking.
However, the counter argument to ENCOURAGE the spread of determinist thinking for its supposed societal benefits, is an even more flawed claim, as point 3 is a drastic overstatement of the evidence for determinism, and 5 (due to 5b being untrue) is invalid.