Heh, most of the fights I ever got in were in the context of a competitive sports team. There was always informal refereeing; other people on the team pulling the fight apart when they decided it was over. And there is an unspoken code of conduct; putting somebody in a headlock ended the fight, and you would never try to do something insane like gouging somebody's eyes out.
Of course sometimes a small minority of people are insane and decide to maim and murder people. But I don't think "zero tolerance" environments are good at suppressing that. These policies are ineffectual against psychological/social bullying; how do you prove anything about a maliciously planted word-of-mouth rumor? That stuff goes unpunished, and that sort of bullying does more long-term damage than a typical schoolyard fight. Those festering social wounds probably drive more people to homicidal insanity than anything else.