> This entirely sidesteps the issue, which is that if you employ a compatibilist notion of free will (in other words: a "free" will that is merely an illusion of agency), then you have no actual agency, and so assigning you moral responsibility for the actions taken is fundamentally unjust and in itself wildly immoral: You had no actual control of the choice taken.
Except that's irrelevant. The fact that a murderer had no "ultimate" control over becoming who he is, is irrelevant to the fact hat he felt justified in committing the murder, and the entity that feels justified in murdering has made an unethical choice, and so that entity requires correction. This is the inescapable question free will addresses: who is responsible for a choice?
And this addresses your claim here:
> This entirely sidesteps the issue, which is that if you employ a compatibilist notion of free will (in other words: a "free" will that is merely an illusion of agency)
So this is not an "illusion of agency", this is exactly the kind of agency people care about: if your thoughts and feelings counterfactually determined your choice free of coercion, and if that choice was wrong, your thoughts and feelings require correction via feedback, which is holding you morally responsible.
> I'd also strongly content that you're wrong, and that if you actually dig into peoples beliefs about free will deeply enough to ensure they understand what you're suggesting, you will find most people get annoyed, agitated or outright angry at even the notion that they don't imbue outcomes with some magical fairy-dust agency they can't define.
You can contend strongly all you like, I cited empirical evidence that was part of a series of studies undertaken over years which tested to see whether people have Compatibilist and incompatibilist intuitions. People agreed strongly with Compatibilism after it was properly explained to them, which is the opposite of what you claim.
> The exceedingly rare compatibilists I come across tends to be a small subset of the exceedingly few people who read philosophy papers.
Well then you're in for a shock, not only from the paper I linked above, but also because a comfortable majority of philosophers who actually read and write philosophy papers for a living are Compatibilists:
https://philpapers.org/surveys/results.pl
EDIT for your edit:
> I'd love to see a survey ask people if they think a purely deterministic process, e.g. a suitable program running on a computer, can ever be said to have free will. If people say "no" to that, they are rejecting a compatibilist definition of free will.
We already know the answer to this: anthropomorphization is a near universal cognitive bias, by which humans assume a mind behind phenomena, particularly phenomena that exhibits complex behvaiour. This is why people are polite when conversing with chatbots like ChatGPT.
If there's a mind that's responsive to moral feedback as I described above, then it makes perfect sense to hold it responsible, and I am 99.9999% certain this is how most people would treat this question.