Hence why it's totally frowned upon to use exchanges that requires KYC, because the potential leaks could be a lot more destructive.
the problem is that most reputable exchanges require kyc. You have to verify your identity especially when withdrawing big amounts of money.
Exchanges that do not ask for identity verification usually have small trading volume and you can't be sure if your funds are safe with them or not.
You're right, but Bitmex doesn't ask any KYC in fact. You just need to provide an email address to open an account and to trade whatever amount of money you want. So only your e-mail address is at risk there, no other personal information.