You make reference to 'our current beliefs', but there is not a unity of belief on animal welfare. Witness the various limitations and protections on kosher/halal slaughter in various parts of Europe. If modern discourse had a single standard here, we could harmonize the views of 'a painless death' with the kosher/halal view of 'a quick and merciful release from a healthy state of being' by appealing to some clear, shared, central standard.
But both are operating, current standards for what is humane, held by actual people in Europe. (Not the center of the universe, but hopefully among this 'us' of yours.) From the pro-restriction point of view, the pain of the knife should be dulled by drugs or electricity to make the death painless. From the point of view defending kosher or halal standards, that just means the animal is not healthy and happy for as much of its life as possible, right up as close as is practical to the moment it dies. From another, moderately paranoid version of this same notion, the meat is no longer 'natural', as it has been handled unnaturally, and we do not know with certainty whether or not it may be less than healthy to consume.
Clearly brainless chickens would never be happy, and would always be painless. But they might also never be healthy, and they would clearly not be natural. So I would say theories about them bother us because we are in fact insecure about what those four things have to do with humaneness. But we should not pretend there is already consensus.
Given just the four concerns raised here, there are a range of relevant questions. Many of us in the U.S. used to regularly eat chickens that lived too close together to be healthy without a continuous infusion of antibiotics. Was that a moral change? or just a protection of the continued power of our medication? It felt moral to those who proposed it, but most of us really did not care until the latter issue became relevant. If we don't want sad chickens, would we eat a chicken that was happy only because it was on the chicken equivalent of 'catnip' its entire life? Do we care about naturalness in that way? If we value naturalness, we clearly cannot make a chicken's entire lifetime painless, as that would be unnatural, so why do we focus on giving it a better death than nature would?
From a Kantian point of view, behaviors that restrict future extension of compassion should be avoided, since universal compassion is a necessary component of the ethical process. So natural sentiments like this matter, even if they are not rational, but merely project human concerns onto other species.
The question becomes whether the kind 'weirding-out' and subsequent 'getting-accustomed-to' that brainless chickens would require would make us less sensitive to other animals, and ultimately to humans, or whether our current habits of interacting with actively behaving chickens already do this to a greater degree.