There is totally a missing mood around Nazi punching. It’s not “I hate this, but punching them really seems to be the best option right now, so I’m gonna go punch a Nazi and then probably feel guilty even though I think it was right”. It’s “punching Nazis, fuck yeah. Nazis are bad, it’s great to punch them. While we’re at it, let’s punch people who support Nazi free speech rights. Surplus to human requirements! Nazis are bad! Punch punch punch!”

So yeah, it really doesn’t sound like you’ve done a cost-benefit analysis, and put “a person gets hurt” as a negative that gets outweighed by the positives. It certainly doesn’t sound like you’ve done that taking into account the possibility of motivated cognition and the dangers of normalizing violence. What it sounds like is you just want to punch Nazis.

That’s understandable, but you don’t get to punch people just because you want to.