Could anarchy actually work?

No. there are always some people who take advantage of other people, and if the is no government to stop them even people who now follow the rules will start to also. That is they see it as a choice between being a victim or a victimizer. You see it everyday in traffic jams when some people start changing lane and cutting you off to get an advantage and after a while more and more people do, but if there is a police car around people take their turn to get through the bottle neck.