Does it make sense to hold a rock morally responsible for falling downhill due to the law of gravity and crushing somebody's head? Likewise, does it make sense to hold humans morally responsible for anything in the absence of libertarian free will?
Even if there is no such thing as "free will", it is still important to give punishments, even if people cannot help it. For example, if someone is seriously mentally ill, it is not their fault, but you have to guard them to make sure they don't hurt anyone. Likewise, we hold criminals "responsible" for their crimes and imprison them to keep society safe. We also let people deal with problems that they were fated to end up in because we can't help everyone, and by wasting resources to help everyone, we ruin everyone else's fates that were fine before, too.
TLDR: we can definitely hold people responsible without free will, wether or not they are morally responsible is irrelevant.
If you saw a rock falling on somebody's head, you would no doubt take two actions:
- Inquire where it came from, why it fell and make sure it does not happen again, possibly by physically holding the remaining rocks with a net or adding some barriers in the way to prevent people from accessing the danger area, or at least be warned (prevention of reiteration).
- Assist the injured person if they are still alive, or at least signal the accident to make sure the body is properly taken care of, the family informed (mitigation of consequences).
Let's climb an echelon in the scale of consciousness: what if a stray dog bit you unprovoked during a walk ? Without supposing the dog is acting in free will (most people don't, it might be, but we will see it's irrelevant) you would probably take the necessary steps to your protection by keeping it away from you in the future, putting it in cage or killing it. After all, this stray dog bit you, it might do it again on your next walk, and you would be fully justified in not wanting it anywhere near you. You could also tame it, to make sure it does not do it again. You would also surely proceed to mitigate the damage as described above.
Now what if someone committed a crime against you, like punching you unprovoked or robbing you ? The same steps of preventing reiteration and mitigation do apply, wether this person did it freely or not.
This person has shown a disposition to wrong you once, they might do it again. Even me who haven't been wronged but saw it happen, i might think that this person would wrong me too if they had the occasion. We would be fully justified in not wanting this person near us in the future, or wanting their behaviour to be corrected in some way.
As for mitigation, contrary to the rock or the dog, this person can understand the damage they done, be reasoned with and then be required to help in the mitigation. For exemple in the case they injured you, they might be required to pay for all or part of the damage caused. Damage has been done, and someone will have to bear it. The default possibility is you, the victim, bears it (no mitigation, or mitigation by your own means only), otherwise the wrongdoer could bear part of it, or someone else. You, me or the other people in society have done nothing to hurt you, and it would be unfair to require us to pay for the mitigation (we still could participate as a courtesy, but forcing us is unfair). On the contrary, since someone has to pay, it seems fair that the person who did the damage is penalized for repairing it. The penalty of sacrificing part of their income or available time to repair the damage will also participate in preventing reiteration.
So as you can see, without mobilizing the idea that the culprit acted in free will, we are justified in requiring their isolation and/or re-education (jail for immediate isolation, community service or a fine can make them think twice before recidivism, education while in prison can help reinsert them in society, etc) and their participation in repairing the damage they caused. To the contrary, if we assume they did not decide freely to wrong us, but they were determined to do it by their disposition or the circumstances, we can conclude that they are all the more likely to do the same thing again if left in the same disposition or circumstances.
Here I concentrated on criminal cases, but the same reasoning can easily be applied to more petty offenses: if my friend hurt my feelings and is likely to do it again because he shows no remorse, am i not justified in preventing future hurting by breaking up him and looking for better friends? If racist uncle Joe ruins the mood at each Christmas eve, am i not justified in protecting my fun by not inviting him anymore?
We don't need to mobilize the concepts of good and evil, invoke the fact that a wrongdoer is wicked or morally flawed to punish then and/or ask for reparation. It is to say, we don't need the idea of libertarian free will to hold them responsible of their actions.
Wether it makes any more sense to hold them morally responsible when we can already hold them responsible in fact, i think it is irrelevant.
Addendum: the idea that free will is necessary for responsibility is often followed by the argument that "we need free will to hold people responsible, so no free will no justice system, therefore free will must exist". It is a very bad argument. I think I have shown its premise is false, also even if it was valid, it is an appeal to consequences. One's desire to hold people accountable has no bearing on the fact that we have free will or not. Facts don't care for our feelings.