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Surely this is a common sense now for most of the people and knowing that you are even leaving out personal information just for the sake of being able to register is quite concerning. If I can recall correctly, there was also a data breach back then in Binance and regardless if it was true or not, it is still alarming nonetheless.
If the security of your personal information is really important, the same could be said for your money regardless of how reputated the site/app is/was. There is no perfect security since everything has been coded, made and maintained by someone.
From my understanding, there's nothing bad in making use of CEX or providing your personal information that's if the CEX is worth it and for the record, there's no way we can exchange crypto for fiat without the use of CEX unless we have someone who can do P2P trading with us.
Having said that, keeping crypto on an exchange CEX or DEX for the long term is what I don't support.
The issue about the Binance data breach if I could remember correctly happen through a phishing site, telegram trick, etc and the hacker was able to get user 2FA codes, API keys, and important info that Binance didn't state how important the information are.