Data privacy is becoming a huge challenge in the world not just in the crypto space, but talking about data safety in centralized exchanges is a long discussion because there are many things to put into account. First centralized exchanges have enough volume and good user interface and this makes them very attractive unlike its counterpart decentralized exchanges, thus to enjoy more trading in most exchanges like Binance, you will need a verified account. Also, most centralized exchanges now supports fiat withdrawal and the first step towards withdrawal is having a verified account, thus you can see most times users have no choice than to do what they have to do in order to make it easy for them. And lastly, centralized exchanges most of the times, acts on the directives of the law enforcement.
But however, all these doesn't outmatch their incompetencies in securing users data thus should take full responsibility for their failure in that. This also means that, users should at all times take every step to protect their data, in whichever way they can, there are good Dex, P2P platform are also there etc.