Dex already support fiat-crypto trading in the form of stable coin but to cashout those stable coin you have to trust respective entities who have created those stable coins so it cant be trustless and fully decentralized. So called Government backed coin after launch will be just similar to existing stable coin with more regulation and they might even keep their blockchain private.

In future, i doubt even these dex will exist. They might be shut down by regulators just like how they busted coin mixers.