> after receiving a punch ... maybe they’ll become better people.
That seems like the logic of a supervillain or sociopath. "When they did something bad, it's because they're a bad person that I'm allowed to hurt, but when I'm violent it's because I'm making the world a better place."
There may be times when that works, or it's the least bad option, but my instinct tells me that the sort of person that most deserves a punch is also the sort of person who is most likely to respond to that violence by doubling down and hurting more people (their victims often being those who can't defend themselves).
I punched a bully in the stomach at school (after many months of the school doing nothing to address it), and after that he completely left me alone. It was a small school, so I'm fairly sure he didn't move on to anyone else either. A few years later, we even became friends, our younger siblings (5 years younger in each case) become friends (without knowing about the incident in question), and since starting his own company has done paid work for our family (which we wouldn't have allowed had there still be any animosity).
I've no doubt violence begets violence in most cases, but it can also improve the situation for both sides in others.
The legal term you're looking for is "serious bodily injury". Reasonable expectation thereof is the threshold for the use of lethal force in self-defense in most US jurisdictions, for example.
That seems like the logic of a supervillain or sociopath. "When they did something bad, it's because they're a bad person that I'm allowed to hurt, but when I'm violent it's because I'm making the world a better place."
There may be times when that works, or it's the least bad option, but my instinct tells me that the sort of person that most deserves a punch is also the sort of person who is most likely to respond to that violence by doubling down and hurting more people (their victims often being those who can't defend themselves).