Centralized exchanges being regulated is not a bad thing, so many of them do shady things for profit and they control their customers' keys and personal data, if they are not regulated they can use this money and information in the wrong way.
1. Have you forgotten that it's human beings you are dealing with? Crypto aside, it's a matter of time before they would hide under that to launder money.
There should be services people can use if they don't want to hand over their privacy to data farms, the government don't have to attack all the available services that provide privacy because they want to stop crypto money laundering, they know how easy it is for people to launder money with cash, so they know what the real problem is.
3. What if they just disappear with the customer's money?
If it is a decentralized exchange like bisq, you send your money into a multi-sig wallet controlled by you and the other trader.