If there is one thing i don't like to eliminate from most proposed or projected ideas is the possibility of it happening but this one, a crypto system completely eliminating and replacing fiat, i doubt its possible.  Fiat doesn't just stand as a medium of exchange but then, it serves as a nation's national symbol. One thing that crypto is not prepared or can't be because, it would be bringing some centralization into the system.
The best we could hope for is crypto and fiat to work in along side each other. Besides, as it is now, its been one way treasure the crypto value and its working quite fine.