Well, that's the common thing that usually happens in new exchanges these days but why would someone use the untrusted exchange as a wallet?
Even trusted exchanges should not be used like you said, only trading funds should be on exchanges, after trading, it should be sent back to a noncustododial wallet.
Even if you are using Binance I still wouldn't recommend it to use as a wallet because anytime there's a huge risk of losing your funds that you can't do once it's gone. We have free wallets online like electrum or you can buy a hardware wallet like the ledger nano.
Not only Binance but also all other centralized exchanges, they have the complete control of your own asset.
And I believe that most of these days exchanges nowadays are becoming more centralized that they tend to ask KYC to all of their users and I think we can't help it once the government regulation tried to make all exchanges accountable like banks. lol
Just that the exchanges are even centralized before, just that the KYC requirements is becoming stringent than before.