Addressing the "privacy" issue on DEXs, should be a piece of cake. Especially when we now have ZKPs (Zero Knowledge Proofs) capabilities both on smart contracts and on the main Blockchain itself. There's nothing stopping developers from creating a truly-decentralized DEX with privacy in mind. It's just that there's not much interest in this. The general public is satisfied with existing solutions. They prefer convenience above all else. It's why centralized exchanges are the dominant force of the market.
Developers can actually make everything private, but do new crypto users care about their privacy? This is where the problem lies, and that’s the reason why centralized exchanges are everywhere, and the government will keep controlling them which might result to controlling each and every user of crypto since so many crypto users prefer the use of CEX instead prioritizing privacy by using the DEX.
The problem is always on the legal side, the DEX have people working behind it and many of them don't want to get entangled into problem especially matter of anti money laundering.
They could easily route every swap through ZK shielding but they will need a lot of money to get the best lawyer to defend them in court.
Unless there is a regulation that could make it clear, separation of responsibility between DEX developers and the user who might intentionally do unlawful things, the privacy issue won't be addressed.
That's the thing, if you build a DEX, you should not be responsible for it, or in charge of it. Remember, this is called a DEX, as in DECENTRALIZED exchange. Meaning that if someone can stop it, or do something about it, then it is not really decentralized.
So if they are not decentralized, that's bad, if they are decentralized and governments wants to prevent, they can't, because there is no ownership. So either way is bad for the creator of it, you either have no access and you will be harassed by the government, or you do have access and you are a liar.