Well, every single citizen in a capitalist society has the POTENTIAL to become a powerful/wealthy person. So to anarchy, I cannot see humans thriving in that kind of society.

When I mention anarchy, I refer more to anarcho-capitalism, not anarcho-communism.

Tell me one successful (civilized) area where anarchy is present! Capitalism will always be the best to me because of the potential available to every single citizen.

How do you measure success? by the number of bodies one murders in order for their nation to reign supreme? Western capitalism, or better..corporatism, has been raping the entire planet for over 3 centuries in order to be "successful".