Every anarchy in existence in history and in the world today result in a bunch of warlords fighting for domination, those petty warlords are either plain dictators, communist dictators, or theocrat dictators.
Nobody else gains any traction, and the absolute worst of things happen to people.

that being said, unlike the communist utopia (which is a nightmare), an AnCap society would be a true utopia if it manages to exist. But for it to exist human nature itself has to change... or perhaps a pseudo religion based on it has to occur with very zealous followers, enough so that they will spontaneously form into volunteer armies to crush threats against their society.