IMHO I believe their will be a transformation where there will be a hybrid of Crypto / Fiat currencies when adopted by the masses. Then the next logical step will be for the various FIAT currencies to adopt Blockchain technology as the underpinning tech to drive FIAT currency generation which will be pegged to the existing FIAT currencies. The interesting fact will be to see if the value of the FIAT's can be sustained. I do not believe it will be possible due to the fact that Blokchains are transparent, immutable and trust-less. There won't be much room for corruption and other things.
The outcome in my opinion will be that Crypto's will and should surpass the FIAT currencies.
So far the Chinese government has implemented Ant shares an ecurrency. Putin and Russia has announce their intentions to follow,suit. I keep reading about Fedcoin coming from the Federal Reserve. This happening very fast...
Their are also various countries in Western Africa, which have already started a Blockchain underpinning their pegged FIAT currency in a digital format.