Private property ownership would act like a like an organism with a common goal and the individuals acting in their own self interest would collectively reject them. They would likely eventually end up in a desolate unclaimed wasteland where they belong. If someone wanted to take them in they could but usually doesn’t go well.
Discussion
OK, but outside one's community, one would be very vulnerable to attacks. I am theorizing that there would be Narco/Mafia communities with lots of resources that would be interested in taking over honest people's communities. The only way to counter those offensives would be to become a mafia communityads well. I believe that it would turn into a deadly free for all in no time. Don't get me wrong, I believe in what your are saying, in theory. However, I feel it would be impossible to implement in practice. Or at least in a way that would be worth living.
Private security.
The world is a deadly free for all the time. But productive people that don’t have their wealth stolen by government (warlords), aren’t told what they can and can’t do by government, can live much more productively and naturally. Defense of private property is simple and natural at the individual or familial levels. But hiring professionals would mitigate warlords in a free and open society.
It is easier and more profitable to defend property than to try to take it. So defense companies have an asymmetric advantage and can outcompete (and make profit doing so) attackers.
But that should be so for the entire planet. Otherwise the Russians, Chinese, Martians, whathaveyous, would come on their Migs, aircraft carriers, nuclear subs, spacecrafts, and take the communities reliant on private security. This can only happen with worldwide consensus which I believe impossible to achieve. I feel it would be easier to have a Chinese style dictatorship worldwide, enforced by mass surveillance and Ai, than to have communities like you are describing. This is what I dread, but I feel the world moving in that way.
And for saying this shit I will be among the first sent to the fucking mines
Narcos don't have the numbers or the firepower to take over a community unless first a State both disarms the victims and then fails to protect them.
Look up clan / tribal / frontier societies anywhere.
The American West had lower murder rates than the cities of the East, despite being a worst-case-scenario in almost every way...