That's not predestination, but it comes down to the same kind of thing.
In general, I think all forms of justice in the west are based on free will being true. If some form of determinism is true, then "punishment" doesn't make sense.
Isn't that backwards? Believing that someone is inherently bad is effectively equal to them having no free will and their fate being determined. You can swap out "born with an evil soul" for "genetic predisposition and early environmental factors".
If you really did replace the judicial system with one based on the view that free will does not exist, would the solution to habitual criminals be to simply separate them from the rest of society for life since they have no ability to determine their own actions? If instead you think they can be externally influenced by rehabilitation then how is this different from having a compassionate view of criminal behaviour that could include free will? Having free will doesn't mean that a person will always make the correct choice or even the moral choice, we're limited and imperfect after all.
I don't think removing punishment is a cure for this. Excessive, cruel or needless punishments should not be applied but you do need to impose some cost as a consequence. Human beings are capable of learning and both reward and penalty are necessary for that to happen. If we are going to push a lever it should be focused on effective rehabilitation, which would involve a complete overhaul of and a lot of investment in prisons so they can address the needs of every inmate.
That doesn't really follow. If you know you are going to receive punishment for some action, or that you have been punished for some action in the past, you can completely deterministically "decide" not to do something you would otherwise have done. I mean, we build AIs that nobody would claim have "free will" and are entirely deterministic based on their algorithms and input based on the same principle.
Some sort of ineffable moral element of somehow making your free-willed self a "better" free-willed self may be removed, but the sheer brutal pragmatics of "other entities want your behavior to be thus, and by applying punishment can increase compliance" works just fine in a deterministic regime. And to my eye, our ruling elites are in practice very, very concerned about the latter and do not give the slightest rip about the former, whatever their beliefs about "free will" may be.