Humans are tribalistic. We form hierarchical societies spontaneously, so I don't think anarchy would last long before being replaced with some form of government. If anarchy could be sustained then I think it would fail for the same reason that every other system of government has failed: We are inherently are selfish.
Crime is punished to disincentivize crime. Unfortunately, high-profile criminals often outrank the courts of law. I think that good education and parenting are excellent methods for decreasing crime. Children who understand morality will often carry those morals throughout their life, or even expand upon them

I suspect that a child who is treated with fairness or respect is more likely to treat others with fairness or respect.
I agree that humans seem to spontaneously form governments. Even in small groups, people seem to choose a leader. Either that or the leader just chooses himself and nobody complains. I'm wondering how the parenting part and crime is connected to anarchism. I guess that in anarchism there wouldn't be an official punishment for crimes. You are concerned that if there was not judicial system, criminals would be rampant? I agree that children who are raised well will be more likely to do good as adults, but how does that relate to anarchism? Wouldn't that be true in both anarchism and other political systems?