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.
It is not being eliminated but it is also the reality that we cannot refuse the power and the value of digital currency in our society as almost all people are happy to use digital currency more than fiat we they found it reliable and easier than all other investments, we should have admit now it is modern age and digital system is ruling in the world, so the age is reducing the use of fiat currency itself.