What happens though, when you get a fiat cryptocurrency?

Part of the reason China has been banning bitcoin, closing exchanges, banning mining etc, is because they're launching their own official stablecoin, pegged to the renminbi. They have started trials already:

https://www.cnbc.com/2021/03/05/chinas-digital-yuan-what-is-it-and-how-does-it-work.html

Basically they've given wallets with starter coins to the people in the trials in Shenzhen, Chengdu and Suzhou. And they're tweaking it to see how it works. Eventually it will get rolled out everywhere - and there will be a lot of people using it because it is convenient and it's value doesn't swing about like bitcoin.