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.
Today you cant be sure if your funds safe at bigger Excanges too .
We have seen that in the past and i have felt this 2 times now in the past and
i advice all that you just deposit so much coins what you want to trade and after that withdraw it back to your wallet.
But if personal Informations got leaked from exchanges its terrible.