Having zero governing bodies is a thought experiment laid out more than a few times in Sci-Fi, so assuming those weren't totally wrong, I don't think the human race can do without. The problem are humans and their motivations. Greed is one problem, laziness another. I don't know how to solve those. How do you make sure people do not exploit their freedom by making others suffer?
Okay, let's say there's no governing body. Now, there's a dispute. How is it resolved? Fight to death? The achievement of modern society is that we do not kill each other, and that requires rule makers, rule enforcers, oversight to keep chaos down to a minimum. If we do, it's a punishable offense. But punishment as implemented right now is totally wrong and doesn't solve anything. Putting people away for years does not make the crime undone and also doesn't turn a killer into a pet store owner. There are experiments with different kinds of containment and reintegration into society but this is also a hard problem that's unsolved.
I honestly don't know how without some sort of management entity a peer to peer society would work without rules of any kind.
Once you enact rules of conduct, you have everyone follow the rules, and something somewhere needs to make sure rules are not broken unjustifiably.
It's like distributed systems or cooperative threading, if you think about it.
Can you tell me how you'd do it?