If all of the fiat money was replaced by digital I think the corruption and criminality would arise. It would be more difficult to track down transactions. No one will know who owes and what money, which might lead to a chaos. How do you expect accountants to do their job, if all they knew about a certain bank account would be a bunch of characters? And, also, if every fiat currency was replaced by digital, but still it would be the government, who regulates the system - then what about all of the alts and BTC, that we use now? Would the governments let people use it then? I don't think so. And what about the taxes? Anyway, I don't think that there's any point in changing all of the fiat money to cryptocurrencies.
If ever cryotocurrencies completely take over and replace fiat, there is no way that the government will allow such as the things you are saying. There will be a way to track down digital money because there is no way that the government will not regulate it.
Btw, even with cryptocurrency we are still paying tax. Even at this moment.
And there is a very huge possibility that by the next few years, people will then prefer transactions made online or usung digital money for convinience. The world is fastly evolving and so is the technology.
In such a case - either the whole economics will crash, or cryptocurrencies won't be anonymous and won't have most of the advantages that they carry now anymore.
I can't imagine the whole economic crashing. Surely experts can do something to prevent this. As for the current adavantage and characteristics of todays crypto, I agree that soon it will change accordingly to what is best suited once crypto take over the world. I'm sure there will still be versions of crypto in the future which can be used with anonimity.
Taking the lead over the regular currencies is not something which you can expect to happen in a day or two and that this is something which will take a lot of time. However, the way things are happening and that they are turning in favour of the crypto currencies can give us a great hope to believe in this thing that these crypto currencies will then be leading this world in much better way.