Though it may be true that fiat fails, fiat has been with humanity for as long as humanity has economy in their culture. That being said, fiat is a hard economic system to remove or even exchange with something as new and volatile as crypto currency. It would need time and alot of patience for this to happen.
I agree on that, fiat currency might fail someday because people will prefer to invest on on bitcoins but government will still do something in order to reduce the number of investors of cryptocurrency.
Very honestly I do not think that it is going to happen, I think that it will take a lot of time may be more than half century when people will totally stop using their fiat currency and will use bitcoin for everything for which they were using bitcoin.