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.
I used both exchange Coinbase and Binance with KYC verifying level 1, not submitting proof address or bank verifying regarding both exchange available for trading, withdrawing by verifying only level 1 document ID.
I don't think worry about document ID submitting at Binance or Coinbase exchange because our document keep secure and not publish yet for selling at dark market, I can't remember how many scam exchange previously from FTX, Hitbtc, Bittrex, Hotbit but never found any exchange sold their user document to dark market.
I don't know why many people scare about using CEX exchange after regulation must verifying document ID, every exchange have follow government regulation by verifying document ID how to protect from money laundering trough cryptocurrency transaction, by verifying document ID its clearly and difficult for any people to make money laundering trough cryptocurrency.