There is no true delete button in the virtual or internet world. So I don't believe Binance will erase your information although you delete the account.
You can believe or not in the Delete / Erase button on the Internet space but in real life, all documents will be stored for a while. In any agency, any personal identity document, certificate, QA/QC documents will be stored for a while (should be years) before they will be burnt out. When you leave a company, all your records in that company will never be erased from their database after one night. It takes years to be completely erased or it will stay there forever.
We don't know companies whether will follow the rule on Internet space but if will do follow that rule, a few years of storage is risky enough.
Example is Binance but you will find similar terms on other exchanges in their ToS.
If that question about privacy, then still you are at risk. When you use your card to buy Bitcoin means you already expose your identity. Create an account then buy Bitcoin and delete, mix, and so on is too much harassment. And you have to spend fees for that.
Don't submit your identity for KYC if you're worrying about risks.
If you struggle then you may buy peer-to-peer or from your local exchange. Once you come to the centralized, then you can't save your privacy by the way.
Not all peer-to-peer exchanges don't require KYC.
Bisq.network is one of non KYC P2P marketplace but their volume is not high.
