If you’re curious about these things, it’s fair to ask of course: Why does the exchange really need your data, what do they do with it, and who actually gets to see it? These are important questions to ask for anyone using a crypto exchange today.
As far as I'm concerned the only place your KYC data is actually safe is with you only. Basically most of these companies claim to take good precautions and measure to ensure that your KYC data is safe however most of them don't really store their customers KYC data properly and in the end some of them gets stolen by hackers or being sold on the dark Web to use as an edge to gain information to scam people.
Every now and then you see cases of people being scammed on exchanges like coinbase and if you noticed you wonder how this hackers are able to target the exact people to scam.