Most people don't even shoulder their share of household chores, even though fair sharing is enforced by informal yet powerful social mechanisms. So I'm not optimistic regarding widespread peaceful anarchy for services.
Fixing potholes yourself also takes a (few million) step(s) backward in time: it's the bartering of public service, forgoing the awesome benefits of specialisation and cooperation.
But you know where this sort of anarchy basically works: taxes! Almost all people send in their tax returns without a fuzz. It's almost as if they agree that everyone should chip in for shared endeavours, and that money is an excellent medium for coordinating it all.
(yeah, I know there's the threat of criminal law lurking if you don't pay your taxes. But taxes are probably the world's most universal policy, and only a select few lunatics and presidents seem not to get the concept)