No centralized exchange is totally safe to use for everyone, and most of them had some hack incidents in past, including Kucoin.
Never hold coins on exchnage long term, only use them for trading.

Or you can just create new Kucoin account with new email address, that is if you don't have any coins left there.
That trading password is single point of failure and they had to protect it somehow, but I don't think that kyc is a good idea.