I mean, first of all, have you taken a look at our current society, and second of all, this is just a thought experiment to prove that anarcho-communism is pure fantasy, or at the very least not inevitable.
Anarcho-Capitalism cannot exist, it would cease to exist the very second it did.
Anarcho-Communism is a lofty goal, but is fully capable of existing.
That's the fundamental difference, what you consider to be Private Property simply wouldn't be, it would either be personal property or you wouldn't have it. It is only through threat of violence that one can own the products of tools despite not doing the labor.
Okay, as frustrating as it is to have you simply repeat your initial statements despite any arguments made to the contrary, it seems as though your point hinges on the distinction between personal and private property.
However, I don't see how private property couldn't be maintained as long as you have the ability to defend it. Hiring guards for instance does not constitute a monopoly on violence, since others can do so as well. In an anarcho-communist scenario, for instance, if the workers want to maintain control of the means of production after ousting the owner, they would potentially have to post guards as well, or the property owner could hire a bunch of mercenaries to take the property back.
The long and short if this is, I don't see how anarchy would favor either the creation of capitalist or communist structures of organization. Most likely, there would be both, and survival would be a matter of who is better at organizing.
There are numerous critical flaws of what you just said.
Why would Guards support you? If you become a robber-baron, hiring muscle to protect your factories from the Workers, you have to deal with the fact that either you don't actually control and own your factories, the mercenaries do, or accept that you have become a micro-state.
What is preventing any of these micro-states from absorbing others and becoming a full state? Nothing.
Why would anyone willingly work for you, unless it already reached the point where you are essentially a state? They could make more money simply by working cooperatively.
Private Property cannot maintain itself unless you have a monopoly on violence and thus a state.
Cooperatively owned property, on the other hand, supports itself and is maintained cooperatively. There are no avenues to realistically overturn it.
I don't think you're wrong about the idea of micro-states forming, but I don't see how a communist cooperative isn't a micro-state by the same definition as well.
As far as cooperatives being naturally more efficient, I highly doubt that. Centralized structures are far more conducive to decision making. While your commune is still debating about whether both Marx' and Engels' birthdays should be a day off, the capitalists are already working.
Also, the idea that property somehow magically supports itself by virtue of being communally owned is complete fantasy. You clearly have no actual experience and are just spouting off a bunch of dogma you've read somewhere.
If everyone has equal power, there's no statist component.
Cooperative structures are not inherently more efficient, but Cooperative work structures would result in higher paid workers. The strawman about a lack of decision making in the Cooperative could easily be flipped, while the Workers are already producing, the Capitalists are figuring out how to extort their customers and workers better.
Communally owned property supports itself by virtue of being communally owned. If nobody has an individual claim to it, someone who tries would be contested by the community, hence its communal ownership.
You only have strawmen and vibes, no actual points.
I really hope you get to fulfill your dream of living in a commune one day so you'll have some actual first hand experience of what you are talking about.
I'd pay good money to see your face the first time you get outvoted on something you think you are absolutely right about.