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.
At the end of the day, we can't be too sure. Not to mention, KYC verification can draaaag a lot and be a nightmare for some if exchanges detected a suspicious activity for instance which can just be a false positive. In addition, threats could come from the outside as well—hacks and data breach for instance.
These are risks, users have to bear.