Presently, I doubt this can happen.
But in the next 10 to 20 years, this may happen.
Currently cryptocurrencies are in a positions where few countries like US and Japan has made it legal and one can do shopping there using it. But a majority of counties have not made it official to use in place of fiat. Though many of the countries haven't made it possible to buy things using cryptocurrency but have given options to trade using banking system. Even currently India and China are not clear with their stand about Crypto.
Certainly we can't see it happening in couple of years but probably in future which would be around next 10 to 15 years we can hope to replace fiat with cryptocurrency.
This is quite possible that people will get options to pay through fiat or cryptocurrency in next 5 years looking at the rate of adoption in many countries. But replacing fiat will surely take a very long time.
At last I would say cryptocurrencies are the future but that to become our daily life we have to wait.
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I think it is possible but extremely unlikely.
For a nation to abandon their national fiat for a cryptocurrency you would need something unthinkable to happen to their financial system. I can't imagine something like being painless for pretty much the entire country.
But is it possible? Sure. I mean, Venezuela seems to be kinda' giving it a go. Their state owned crypto is an attempt to move away from their FIAT and toward an oil backed currency (at least that's the claim as far as I understand it).
There are crypto foundations like Dash who are on the ground creating the infrastructure for a cash system that, for all intents and purposes, replaces their native fiat - however I understand this draws some ire from the government.
But Dash is just one of many projects attempting to do the same thing in many other parts of the world.