It obviously has nothing to do with protecting customers. It is entirely to protect themselves. As you say, sending my KYC to a total stranger doesn't offer me any protection at all. It offers them protection when the government comes knocking and demands proof that they aren't facilitating money laundering, or demands records so they can start harassing people for taxes.

Then you would be shut down, along with every other centralized exchange which doesn't sell out its users to the government. If you want to avoid KYC, trade peer-to-peer on a DEX.

Pretty much. If you have your identity stolen, have thousands of dollars of debt racked up in your name that isn't yours, get a criminal conviction for something you didn't do, do you think the government is going to help you? Of course not. You will have to pay thousands for lawyers to sort it out. The government doesn't care about. All they care about is getting their hands on your money.