He doesn't give you the private key, they usually are held by the exchange, local bitcoins, par example.
You could do an escrow system where you send the btc to a wallet that you need 2 of 3 private keys in order to move the funds. You, the seller, and and escrow arbiter. The seller moved the funds to the wallet, you give him the money and then with his key and your key you move it to your wallet.
In case of conflict, the arbiter can step in and decide.
I am sure with eth you can do even _more_ clever things. Whomever says you can't do trustless transactions just shows lack of imagination.
Yeah but don't you need always need a centralized arbiter to guarantee the exchange? Not verifying the transaction, which of course is done decentralized.
You would need an arbiter, or some system to do the arbitrage, for sure, but it need not be a _centralized_ arbiter. If you kick the can down the road and enough across sufficiently many actors you could get a fair, or, well, at least, predictable, system.
Some sort of voting/staking consensus system might work quite well for this.
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 However both the gatehub USD and the gatehub BTC are IOUs (debts) you can withdrawn form gatehub so you have to trust gatehub to actually own the "backing" and allow you to withdrawn.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.
