As someone who has dozens of thousands of dollars (not in Bitcoin, I sold some of them) on an exchange, what should I do with that money ? Should I ask the website to verse everything on my bank account ?
If you’re on a legit exchange you should be able to withdraw everything. You should never use an exchange as a bank. Have exactly the money on there that you intend to trade with and no more.
It's basically the opportunity cost of being able to trade quickly (xc->bank->xc would take 10+ business days) versus the risk of having co-mingled funds in an unregulated exchange.
The reason banks are regulated in the US is because the banking system pre 1930s wasn't too dissimilar from crypto now.