Now I'm not 100% sure of this because I'm working from memory, but I think Kropotkin gave examples for this in "Mutual aid".

For Eskimos he mentions that anything an individual catches or gathers belongs to the clan as a whole, and then it is redistributed. People living in tribes (with no concept of a separate family) generally live 'each for all'.

Village communities, on the other hand, recognized only movable property as privately owned, while land belonged to the community, and everything had to be done with the consent of the community.

When disputes did arise, they were treated as communal affairs and mediators were found to pass a resolution. If the resolution was not agreeable to one party, the case would go before the folkmoot and the decision reached was final. The party that had to provide some reparation could either accept, or leave the village and go somewhere else, but there were no law enforcers.

A little less rosy than Kropotkin, and not really anarchist, but Icelanders lived without a state until the late 13th century. They had a (bi)yearly gathering (the "Thing") where all grievences could be brought forth before the judges and people. When a sentance was passed, it was up to the family of the 'winner' to see that the other side accepted it, there was no state figure to force them.

I'm very tired and should not be up right now, so sorry if this isn't super coherent or very well explained, but bear with me.

the people doing the raping, stealing, and killing

I do lean very libertarian/anarchist, but possibly my biggest issue with the concept is that you are now assuming that the people who would be targets of the violence would be the ones doing all that.

Having a monopoly on violence is bad, but on the other hand, the alternative sounds like vigilantism, which often leads to witch hunts. I'll bring up a practical example to explain myself better:

There's a streamer on Kick, whose name I won't mention, who streams himself going after (alleged) child abusers. Recently (yesterday I think) he and other people were confronting a supposed child abuser (they just called him a pedo, but I assume they meant child abuser; otherwise how would they know he's a pedo?) but they never showed any evidence of it. He was an old man. At one point a random stranger approached them to figure out what was going on, and they told him the old man was a child abuser. As a response, the stranger punched the old man, who fell backwards and hit the back of his head on pavement. He ended up laying unconscious in a large pool of blood. Rumours say he's probably dead, which doesn't seem far-fetched given the details.

In a lot of ways, having a monopoly on violence that is subject to hierarchies is quite bad, but the upside is that there is generally a due process where evidence needs to be presented, which will lead someone to be put in prison and not murdered - in most societies I know of. This can also be adjusted through laws and regulations. If someone practices vigilantism and murders someone like that, they themselves are subject to that law and might be put in prison. The vast majority of situations don't end up with police killing someone; but knocking someone out (or just down) can very easily end up with someone dying from hitting their head on a hard surface.

Basically, what I fear that a completely anarchical society would fall into a spiral of vigilantism, where people kill each other because someone somewhere said they are guilty of something and most people are incapable of evaluating the situation properly and conducting a proper investigation, and will immediately resort to violence. This becomes even more worrying when you consider that me saying that about the old man situation will make some feel justified in using violence against me, because in their head: "that guy was a pedo, and he's defending him, so he must be a pedo, so he also deserves to die".

Hope that made some sense, and sorry I'm replying to this 4 days later.