The problem I have with the ideal concept (?) of this anarchism is that the police structure we have is 100% caused by simple human nature, and I am not entirely sure what structures could be created that don't involve labyrinthine methods to prevent that force from being human in order to make that work. Every conception I can think of with an anarchic system quickly breaks down into a warlord-driven political structure within a generation, which quickly takes us back to the beginning of the western civilization chain of events.
Not really trying to get into a political theory debate about anarchism here, but I'll give my basic thoughts on this.
This really comes down to what you believe human nature is. I find human nature most commonly used to describe priorities and social behaviors that are believed to be near universally inherent in human beings. The most common candidates are things like greed, laziness, violence, etc. I don't find these things to be common or inherent in people at all. I rather believe that the environment in which these behaviors are observed is taken for granted, and that human beings will behave completely counter to these "human natures" in different situations. So while common wisdom holds that society is made of so many necessary evils in order to contest with human nature, I hold that the things we call human nature are a natural result of the society that we live in, and we wouldn't have to worry about them so much if we addressed the social constructs that encourage features like greed.
The expected counter-argument is that this society is a product of human nature... but humanity has only entertained the core social constructs of civilization for about 2% of the species' history. So that assertion requires some serious backup.
My equally unbacked assertion is that the challenges of establishing early low-tech sedentary lifestyles found certain social constructs to be the path of least resistance, and those constructs were naturally incompatible with other ways of life, which is why they exploded to near 100% adoption by the human race within such a short period. These social constructs are so naturally hostile towards any others that they are eliminated before they can be observed. Because we are never able to observe human beings operating in a different social environment, it's very easy to assume that it must be because the priorities and behaviors our social constructs have us mutually enforce on each other are in fact what's just natural.
But if you take the time to read into the things people do with the scraps of true freedom they have, it's nothing but counter-examples, in my opinion.