But if you use Binance and do kyc there I don't think there will be any problem because they are a trusted and very big exchange platform. So there is nothing to fear about it
Any CEx can suffer data breach. Being big in the game does not necessarily translate there will be no problems.
It's also known that CEx's shares user data to who knows what. In fact, one of the third parties binance used suffered a breach and people's data were leaked, see:
https://cointelegraph.com/news/binance-kyc-breach-did-it-happen-and-if-so-whos-to-blameIn short, there's still a good amount of risk involved even with established exchanges.