To be on the safer side and not lose your bitcoin, because of regulatory compliances, from a centralized exchange wallet, it is better you first receive any bitcoin payment into your wallet, that you control with your private key/wallet seed phrase saved and can restore the wallet anytime.
Nobody should fault what you said in the upper part of your post concerning sending Bitcoin first to one's wallet instead of directly to an exchange. It saves the hodler any unnecessary updated terms and conditions of centralized exchanges we can't run away from. However, we ought to also know that part of the advantages of Cexs is the ease of regaining access to one's account if password is lost or forgotten. This isn't the case with private key or seedphrase of private wallets. Once those are lost, they're lost forever.
The last comparison is wrong and is not a benefit of CEX. You just picked very specific situations to make a bad comparison. If your CEX account is hacked your funds are lost even if you recover it later, that does not help you. It is the same with private keys. Any responsible adult will not lose neither of these 2 things.