In my jurisdiction prison sentences and imprisonment for public protection are different things, and only the latter is to protect innocent people. It is also pretty rare. Most prison sentences are, because society 'thinks' the aspiring prisoner deserves it, not because the public needs to be protected. Also penalties also fulfill the desire of the society for vengeance.
I think, being locked in isolation or with very dangerous individuals can leave deeper scars than a short period of violence. It's also not, like people in general never have any injuries, so it's not the pain itself that is an uncommon experience, but more the knowledge of it being linked to your actions. People don't have traumas just because they walked through nettles, feel from their bicycle or broke their legs.
> And I'm pretty sure the type of person speaking out against outdated, abusive child rearing doesn't support the use of cudgels or tear gas in law enforcement or unsafe/cruel deportation.
That's nice, but I think he still has an amount of accepted violence by the state, because the policy of 'I don't give a fuck, let the strongest do what he likes' doesn't actually lead to less violence.
I just want to point out, how it is not necessarily a black or white thing, I'm not arguing for child abuse.
No, I don't think it is different. Both are applications of state violence for enforcing laws. I think it would be reasonable to use (public) caning as a judicial punishment in the US for certain kinds of crimes, for the same reason I think it is reasonable to use incarceration as a judicial punishment in the US for other types of crimes.