I don't think passports are a good idea, but I do think borders should be protected from parasitic, more often than not criminal immigrants. This would actually fit perfectly in a world with no leadership, as the locals of every place are much better judges of who should be let into their country than any government ever could be. A local militia near a border could pretty much decide by just looking at someone whether that person is a threat to their nation's integrity and therefore should be refused entry. This means regular tourists could come and go anywhere at any time without any hassle, while any parasites will be filtered out effortlessly, without expensive bureaucratic procedures.