You should really look into the Zapatistas. They used civil justice, and were relatively stateless. Also, just because someone talks about anarchism doesn't mean they're talking about being without a process of community involved problem solving/justice. You just need to know what anarchosyndicalism is, or communitarianism, or maoism. The previous user did say "anarchism and communism" after all.
Throughout most of human history "standing armies" and "permanent police forces" didn't exist, they were formed from the community when necessary (and often merely to beat up bad bosses or known criminals).
So the whole idea that society pops out of existence without central command over violent forces - doesn't match up against most of human history.
Rome wasn't defeated by "other standing armies". So no, that's nothing to do with anything..
Also who the fuck cares about recent US history and the wild west. You sound like a dumb ass who knows very little about the scope of politics, history, and the topics being discussed.
Don't rant as cover when you could entertain the possible truths others are telling you: Community policing was the longest form of stable communities.
Not enforced centralized or uniformed violence.