It’s not always advisable for you to receive any form of payment directly to an exchange address it’s at a high risk level, you should always consider the security and privacy before doing that, Binance is a centralized exchange and they are against so many things you never can tell if the address which will be used to pay you from where ever you want to withdraw from is safe enough or if binance won’t mark it as bad address.
To be on the safer side always have a nine custodia wallet where you can receive all your deposit and if you want to exchange it to any currency of your choice you can either use dex exchange that don’t need KYC but if you are not good with that and if you want to use binance only send what you want to exchange and don’t send more than that for security reason and to be on the safer side.
You're exaggerating, when did Binance block gambling funds? I know they're centralized and have a power to froze someone's funds, but it's too far. Remember, even you receive the coins in your wallet first, then pass it to Binance, it's not mean you've hide the source. It's
concealing, nothing different whether you directly or indirectly receive the coins.
Since the @OP don't mind with privacy, as long as gambling isn't illegal in your country, it's okay to use CEX.