Well I do only use 2 exchanges for my crypto they are Binance and Coinbase. For both of those I did do the kyc but I think it is only a level 1 kyc.
I do not worry so much about things like this. They are both real companies and will not steal my coins or sell my information. If they do ask me for more information I do not think I will have a issue to give them what they ask of me.