The most important difference is everyone could create such a group without main authority monopolizing violence. Some would try to recreate current authoritarian relations, while others would oppose them.
It's a nice thought, many small bands of people each doing their own thing. But I don't see why people think it would turn out differently than it has turned out before, which is some groups becoming large and powerful enough that they push out, destroy, or absorb other groups, until they become large and powerful enough that they're just called government.