As Thomas Hobbes beautifully described what in his understanding would be the natural condition of mankind:
"In such condition there is no place for industry, because the fruit thereof is uncertain, and consequently no culture of the earth, no navigation nor use of the commodities that may be imported by sea, no commodious building, no instruments of moving and removing such things as require much force, no knowledge of the face of the earth; no account of time, no arts, no letters, no society, and, which is worst of all, continual fear and danger of violent death, and the life of man solitary, poor, nasty, brutish, and short."[1]
Societies exist as a natural evolution of human connectedness and dependence on each other. Laws as a natural evolution of complex societies attempting to find fair ways to settle disputes. Law enforcement as a natural evolution of societes that come up with laws that not everyone agrees to abide by. The idea that, were we to be left to our own devices would be model citizens is, as you very well put, "demonstrably false fairy tale". The fact that we have laws and law enforcement in the first place is evidence of that.
That being said, ever since I came across the works of Bakunin, Berkman, Goldman, Tolstoy, Camus, etc. as a teenager, I've considered myself very much an anarchist in the traditional and philosophical sense, but definitely not in the cultural sense. That is to say I don't believe that law and law enforcement are incompatible with anarchy: I do share the fundamental believe that all humans are created equal, and that there should be no hierarchies besides those that are natural and organic (e.g. my parents have certain authority over me in the family context, but my parents could equally become my students and I would have some academic authority over them in terms of mentorship, in my field of expertise). Organic hierarchies are the fabric of society and being human. We're not solitary animals, and hierarchies will always form in groups. We can agree that nobody should have any more rights and privileges than others based on claims of nobility, birth, ethnicity, gender, or any sort of social or cultural position, whilst at the same time accepting that in all human gatherings, certain group dynamics will emerge and that's okay as long as we respect each other as individuals and agree to abide by a common set of rules. But I definitely don't believe that humans are good by nature and that society corrupts us -- we are selfish by nature, self preservation has got us here. We're perfect at survival, even if that may mean taking another life, human or otherwise.
I read somewhere that mankind's success is as a result of our capacity for violence. Unfortunately it feels very accurate.
1. Leviathan, Part 1: "Of Man". c. 13 https://www.bartleby.com/34/5/13.html