… So we see, even assuming an “anarcho-capitalist” property regime, anything recognizable as “capitalism” to anyone else could not exist. In fact the society would look a lot like what “anarcho-socialists” think of as “socialism”. Not exactly like it, but much closer than anything they’d imagine as capitalism.
However, under anarchism, even such a strict property regime is not guaranteed. There is no way to impose it on a community that wants to operate a different way. I predict there will be lots of different communities and systems that will compete for people to live in them and whatever seems to work the best will tend to spread. There’s nothing the anarcho-capitalists could do to prevent people from agreeing to treat property in a more fluid or communal manner than they’d prefer. Nor is there anything the anarcho-socialists could do to prevent a community from organizing property in a more rigid or individualistic manner than they’d prefer.
For, just as anarcho-capitalism is impossible, anarcho-socialism is also impossible (depending on how you define things). In reality all of us who are opposed to the state, as that great fiction that some people have a special right to do things that anyone else doesn’t, are anarchists. And what will happen under anarchy? EVERYTHING.