At some level, I think this conversation only makes sense under the assumption that we're talking about a society in which the public is relatively capable of pushing back against outrageous punishments (i.e. a relatively functional democracy).

I should also perhaps clarify that pragmatic, prevention based justice does not preclude punishment for deterrence's sake. The point is just that it's purely pragmatic, not for vengeance, or because the person "deserved" it in some metaphysical sense. It ultimately depends on the public to make sure the laws make sense and are reasonable - that they are effective in preventing crime, but not so severe that average people live in fear of getting sucked into a fickle and unforgiving penal system.

But so in the case of a cold blooded murderer, I think we probably would want them to be quarantined indefinitely until and unless we are confident that they, or their situation, has changed enough that we are pretty darn sure they won't kill again. Whereas with the stick of gum, we probably just want them to pay a small fine, or just keep track of petty crimes in some public record, or something.

The main thing is that, currently, the public largely believes in free will, which I think results in a penal system that is less predictable and more capricious or vindictive than it needs to be. Whereas if the public did not believe in free will, I think the penal system demanded by such a public would be more strictly pragmatic, empathetic, and predictable.