One of the fundamental problems anarchy poses in its most radical form is its insistence on the abolition of property in a world that has a fundamentally symbiotic relationship with property.
Many anarchists scoff at arguments that if there was no government, some other government would replace it. The reality is that a country abrogated of all government is then open to the world property market. An anarchistic people who refuse to recognize international currency exchange would be out of luck if they didn't choose to fight the new landlord. This amounts to a perpetual civil war, assuming that the anarchists in question remain intolerant of the state tenants coextensive with the expanding property of surrounding states. Violence is their prerogative, if they so choose, but fighting forever would, I imagine, get tiring.
What would then be required is some union or organization that could make contracts with the surrounding nation states. Some militia is then formed to protect from invaders, but sometimes the wrong people get shot. Courts are set up to determine how someone might be wrongfully shot. But then the courts get paid off in stolen tomatoes or whatever barter currency would exist, and soon, people start saying that the court needs to be accountable to someone else, and pretty soon, you have a government, in which everyone is accountable to someone else. If things get bad enough, someone is always appointed the leader or a despot takes advantage of the cracks in the system.
This is not to totally discredit anarchy, but rather, to examine why all free zones, no matter how long they lasted, either failed or adopted some model of overarching societal management. Also, the paradoxical border problem explains why most anti-statist movements have been socialist in nature--the free property of the inhabitants is maintained, not by abundance, but is traced by the borders of surrounding empires. Basic needs must be compromised reciprocally from within.
This reveals a more fundamental, ontological character in anarchy which its popular discourses rarely lend explicit enunciation. It is that anarchy could only function in its fullest terms if the whole world was anarchic.
But here's where it gets tricky: the world already is, always has been and always will be transcendantally anarchic, in that each nation organizes itself as it chooses at first, before making itself ever more reciprocally dependent on national defensive contracts which keep everyone from invading everyone else for as long as possible.
The world is already the laboratory. We already know what happens when large scale governance takes place. Perhaps the future will see the borders retract to such a degree that we can see them at the ends of our fingertips.