A DEX is perfectly possible in fact many of them exits. They however don't work with fiat directly because you need a digital fiat with some properties of crypto. So you cant use you bank notes or the number on you bank account unless your bank decided to issue a digital token.
There are other entities that do this for example gatehub issues IOUs for different currencies and tokens https://gatehub.net/legal/xrpl-addresses
So you can own gatehub USD on the XRPLedger and exchange it on the DEX for gatehub BTC. The DEX isnt controlled by gatehub or anyone so its guaranteed fair and whoever sells you the gatehub BTC can not cheat you. However both the gatehub USD and the gatehub BTC are IOUs (debts) you can withdrawn form gatehub so you have to trust gatehub to actually own the "backing" and allow you to withdrawn.
If you dont trust gatehub you may find another issuer. In theory your bank could be such an issuer and then you wound not need to trust any additional party.
Needless to say that no matter what, at the point where your fiat (from your bank) goes "in" or where fiat comes "out" (to your bank) you will need to identify yourself.
There are other entities that do this for example gatehub issues IOUs for different currencies and tokens https://gatehub.net/legal/xrpl-addresses So you can own gatehub USD on the XRPLedger and exchange it on the DEX for gatehub BTC. The DEX isnt controlled by gatehub or anyone so its guaranteed fair and whoever sells you the gatehub BTC can not cheat you. However both the gatehub USD and the gatehub BTC are IOUs (debts) you can withdrawn form gatehub so you have to trust gatehub to actually own the "backing" and allow you to withdrawn. If you dont trust gatehub you may find another issuer. In theory your bank could be such an issuer and then you wound not need to trust any additional party.
Needless to say that no matter what, at the point where your fiat (from your bank) goes "in" or where fiat comes "out" (to your bank) you will need to identify yourself.