I don't think we can prevent all violence beforehand. And I don't think we can prosecute all violence without creating some sort of police or surveillance state.
Given there will (should) be gaps in how violence is policed, we need to give upstanding citizens the ability to handle those gaps in justice in their own way. I'd rather people left the scene, handed over their wallet, recorded and published the incident, etc.
But as another commenter implied by bringing up Mexico, the "let the police handle it" is a bit of a privileged attitude. That isn't a trustworthy option for every American and it hasn't been a trustworthy option throughout American history.
Try that against the Mexican drug cartels and see how that goes
Explain to me how you're supposed to deal with Nazis, or other invading armed force using "Arguments, beliefs, and convictions"
"The police should ...."
Yeah, but the police hasn't, for decades. During those decades the government has constantly moved to further defund the police, not the opposite. So sorry, no.
And yeah, I get it, for the rich in central cities who can isolate themselves on a whim and move houses when they want to, guns are a serious nuisance.
For the poor in a weak position, the fact that 1/10 of the victims are armed with guns is the one thing that defends them. And you personally don't have to participate.
Guns solve short term problems. They don’t overturn tyranny. Arguments, beliefs, and convictions do that.