[Pulcinella]

If the US and other national governments collapsed then every cryptocurrency would become worthless (Gas Town isn't going to accept your "money") or less than worthless (Thunderdome is going to eliminate you because your mining rig wastes valuable electricity).

[nostrademons]

Maybe. My bet is that economic activity wouldn't cease in the absence of nation-states, but rather some other institution(s) would arise that currently perform the function of nation-states: physical security, dispute resolution, identity symbolism, monetary authority, etc. Cryptocurrencies have the advantage of already existing here, but there's certainly the possibility that it could be some yet-to-be-invented institution.