As this has not happend yet, the only thing we can do is "speculate" about the answer.
However, this may change in the near future, Estland is currently creating it's own cryptocurrency.
One of the key advantages for citizens of the country would be that they would have a currency which does NOT devalue / inflate like something as the dollar / Euro, since you can't just suddenly make another billion of them.
However this at the same time is also probably the reason why it will never work.
Countries can't for example "press" more money.
But, the cryptocurrency could also make life easier in the following ways,
Imagine for example if you as en r-resident could charge Estonian customers in estcoins,
pay your corporate taxes and public services in estcoins,
and estcoins is accepted as legal tender in the same way as euros in Estonia. If this actually happens, then there is no limit on how deeply integrated cryptocurrencies could become in everyday life.
Also, it would, if the coin is bitcoin based ( open ledger blockchain.) protect the citizens from their own government.
Meaning they can for example see and verify exactly where their money is going, due to the blockchain.