Not having a fiat currency isn't really as bad as people make it out to be. But we're talking about whether cryptocurrencies make fiat currencies ineffective.

Most people will likely keep using their local fiat currency because that's what credit cards, mortgages, and paychecks are denominated in. A minority (even a sizeable one) using an alternative currency won't change that. Even if most people use cryptocurrencies for transactions, the US can still require any federally backed transactions (i.e. anything touching regulated banks) to be denominated in USD.

A cryptocurrency merely keeps the fiat currency honest. If the fiat is more stable, people will keep their savings there. If the cryptocurrency is more stable (unlikely), people will switch to that and governments will react by tightening monetary policy.

Inflation numbers won't really be impacted because they'll just use some average across money exchanges to figure out the inflation figures for the fiat currency. Inflation is already benchmarked between currencies, so this doesn't change much.

So I honestly don't see much reason for change. If people move to cryptocurrencies in droves, the Treasury will just issue fewer dollars as needed to keep inflation in check.

But what we get in return is pretty great! I can now make international transactions without going through international exchanges, so fees would likely end up being lower. I can use the cryptocurrency as cash in digital transactions to maintain privacy from my bank and potentially government. If I go to a country like Argentina or Turkey, I can avoid day to day inflation. If I go to a country like Venezuela or Cuba, I don't have to play games with black market money changers to avoid government price fixing. I'm also much less likely to get my payment into compromised, so this would make things like virtual credit card numbers unnecessary because attackers knowing my payment info doesn't allow them to initiate transactions.

The main problem is many places don't accept crypto, so that's why I haven't used it much. I'm probably never going to keep a lot of my money there, but perhaps I'd load it up for a trip or monthly expenses or something.