Picking any exchange would be hard, I will give you that much. Even if you are dealing with places like Binance or Coinbase, it could become a difficulty because they require KYC and they could still get hacked in a way that your KYC could be shared with the world.
KYC should be serious problem for us, and why we have to worry about this policy ? isn't we want to maximize our security layer to protecting our account. and passing KYC could help to protect, maybe hackers will have trouble when withdrawing our assets but have different name on bank account and receiver. honestly i am feel comfort if asked to pass this stagge, beside for security reason my account limitation could increase.