If the only repercussion for assault is they need to apologize and "work on themselves", then what's stopping more people from committing assault? There needs to be punishment.
I don't think that people are stopped from committing assault by an abstract risk-benefit calculation that considers the likelihood of jailtime. It's not what stops me, at least. Mostly I just don't want to. And even if I do want to hit someone, I know that that fleeting temptation doesn't accord with my fundamental values; I'll feel bad afterwards. I'm intimately aware that they might retaliate, or that I might accidentally kill them (or vice versa). It just doesn't feel worth it because I've been socialised to weigh up those odds. But the distant prospect of jail time feels abstract and harder to socialise into people in the heat of the moment.
You're not a remorseless psychopath, though. Some people are.
For a nuanced discussion, the Illustrated Guide to the Law is an excellent introduction. Here's the section on Punishment: https://lawcomic.net/guide/?p=41
It ends with the summary "The State punishes those who commit crimes partly in the hope of preventing future offenses (via rehabilitation, deterrence, and removal)... partly to restore a sense of balance and fairness (via retribution)... and partly because fuck you, that’s why (retaliation)"
Namely that it is unlikely to factor into people's decision-making process - and when it does, the extent of the punishment makes little difference. Slightly disappointed to wade through slides of challenging handwriting to find that it wasn't saying much more :/
