The main currency used world wide is also a digital currency, which is dollars.   The vast majority of wealth and of value exchanged is done digitally by dollars.   When banks send value between branches its mostly not done with paper in a secure van with guards, considering all the business that goes on we dont see that many of those.
The paper part of dollar is not that far from the paper wallet you can have with bitcoin.  Obviously bitcoin has its crypto security and dollar is just force and legally enforced but if we are talking digital then yep you are living in a world full of national digital currencies.

Happened a while ago.  The US government would go broke if most value was in cotton notes, they cost more to produce and handle then the worth printed on the front.  The cotton notes are just a way to send money to US farmers now, its a side show.    All the big value is handled like QE is produced, it centres around government money and regulation.    One day we will find out why its not a great idea to have the whole world held up by one central point of failure, finance or anything really.

Bitcoin alone cant replace FIAT but of course it wont ever do that.  Its one of a rainbow of alternatives to the one national currency used globally, remenant of failed Bretton woods agreement (that Keynes guy was present, that you always hear about) which dates back to WW2 now.  Many things have changed since then and so will this also.
   We'll just see green split into a prism of different colours, it was never going to be just a direct replacement one to the other.  Hopefully crypto currency will prove worthy when the time comes and become more popular and reliable in use.