Definitely it won't be that easy for crypto to replace fiat. It's gonna take a long while though, should such is to happen. Whether we want to believe it or not, fiat and crypto will walk side by side. We need the Fiat to spend in our daily lives.
The European Parliaments Committee on Economic and Monetary Affairs (ECON) has come up with a report on cryptocurrency entitled Virtual currencies and central banks monetary policy: challenges ahead. The finding of reports shows that cryptocurrency will not replace fiat currency, even in the long term.
https://bit.ly/2NeLgLr