There is no society that has ever existed where there was no property, and none will ever exist.
This is true. However, the basis for the establishment of property, and what can be made property, can be VERY different in different societies political theories.
I do not believe that the far left consists of people who reject property.
First off, I'd avoid the whole "left vs. right" thing here... we're trying to get away from that with more nuanced vectors/models to show political diversity.
Secondly, check out anarcho-primitivism. It's pretty damn close.
http://en.wikipedia.org/wiki/Anarcho-primitivism
The far left consists of people who believe the current distribution of property is unjust, immoral, or based on theft. They advocate returning much of this property to their former owners, not abolishing the whole concept.
To some degree, yes, but remember, the reason they think it is "stolen" when capitalists see it as "legit property" is because of the very disagreement in terms of what ESTABLISHES property in the first place. Some think that what capitalists of the Americas have deemed to establish property is essentially theft from the community.
In fact, Thomas Paine himself, if you read the quote in my signature, believed something quite communistic about the establishment of property...
"Men did not make the earth. It is the value of the improvements only, and not the earth itself, that is individual property. Every proprietor owes to the community a ground rent for the land which he holds."
This is why anarcho-communism has no home on that map; it's an impossible contradiction. A society with no property norms cannot exist. It is a delusional fantasy.
Anarcho-communism is not a society without property norms. It's a society with
different property norms than capitalism. It's one built on occupation and use. It is one that skeptical of feudalistic style land ownership, where people own stuff simply because they were powerful enough to put a fence around it.
When I talk about models that are nearly-devoid of property, I'm talking about very nearly primitive cultures, where you perhaps own the clothes on your back and a few personal items. Obviously, THIS is a model that is disappearing, but it's on one end of the property spectrum, because land/resources that aren't claimed as owned by one can still be used by the community to form some semblance of a society.
So anarcho-communism isn't really any more self-contradictory than anarcho-capitalism. I think you're confusing communist property norms with primitivist property norms.
Further, your examples of micro-anarcho-capitalism are odd. Simply "exploring elements" of a political philosophy within a Western Democracy can be found in hippy communes.
That's the nice thing about free-ish societies. You can rely on all the stability on the macro scale around you to test ideas that would never really be possible without all that stability... or at least not long before the Mongol hordes come to rape your women & make slaves out of your children.
"Men did not make the earth. It is the value of the improvements only, and not the earth itself, that is individual property. Every proprietor owes to the community a ground rent for the land which he holds."
- Thomas Paine