For one thing, Fiat has been with the economic world as long as we knew gold existed. I really doubt that we can eradicate the use of Fiat anymore than we want to. Maybe we'll use it less with electronic transactions but to eliminate it means that we will use something else (ie crypto currency) exclusively.
Of course we will use crypto when we want to eliminate fiat from the system. Most of the transactions are made into fiat currency and when it enters into the economic system, it will take over fiat currency. Before that time it is not possible to drop fiat form the market. Fiat plays a vital role in the economy but I am sure that we will feel more ease while using fiat.