We know it's the exchange duty to secure user's data but everyone should note that, this data is safe with a third party, hence anything can happen to your data at any point in time.
It once happened to binance when users kyc data leaked in the year 2019, this isn't the first time we are experiencing data bridge. We should be careful when dealing with a platform that requires users information especially centralized exchanges.
Personally, I have two emails. One I used for non cryptocurrency activities, offline work and the one I used basically for online business, multiple registration on centralized exchanges. This way, if my online email is leaked, I don't bother because I don't do kyc since I'm eligible to withdraw at least 2btc in centralized exchanges.
NB: if you are scared of data bridge, use decentralized exchanges.
Yes, if you can just trade without submitting your KYC, the don't submit any doc. Because a lot of exchanges don't require KYC if you have daily withdrawal below 2-3 btc. So just take advantage of that opportunity, unless, you are a big timer in crypto, wherein you need a high withdrawal limit. And when you are talking about local exchange where you need to convert your crypto to fiat, usually they ask for ID, it is better not to submit your passport but other government IDs. We can never be sure about what will happen to these exchanges, even if they are boasting to have tight security protocols. Hackers are getting sophisticated because of the tools that are available now.