A desire for punishments generally isn't for 'enjoyment', but motivated by someone's sense of justice. "Being punished for bad deeds" is a very common notion of 'fairness'.

If your notion of justice doesn't include retribution, that's completely legitimate, but to insinuate that your sense of justice is somehow less of a emotional response than someone else's is ridiculous.

It probably starts with corporal punishment of children. That gives society a baseline predisposition towards violence and doled our suffering in order to enforce conduct. Adults who were beaten as children or felt that they suffered for their transgressions may feel that it’s unfair for someone to avoid suffering for transgressions, when they had to suffer in the past for theirs.

It probably doesn't.

hypothetically, if you could see into the future and ascertain that the perpetrator feels regret and would never commit another crime, should they still serve time?

I would think that there should still be some period of incarceration as a putative measure.

Incarceration is a great punishment by itself, depriving someone of their freedom of movement is already quite a lot. What I meant is there is no need for a vengeful justice beyond that.

If an individual is dangerous for society they shouldn't be in it, this doesn't mean forever if there is a possibility of rehabilitation. There are many monsters locked up that probably should never be released, in that sense the justice systems of Norway, Germany, Sweden and others work well: you are locked up to 20 years, after that your case is reviewed and if you are still deemed a danger to society you get it prolonged, a few times this goes on for life.