Binance and other exchanges also have P2P marketplaces -- I believe you don't need KYC to view these. Many leave their contact details, least last I checked.
But if you read his statement carefully you will see that the OP wants a non custodial wallet that doesn't require him to be Kyced or uploaded any of his identity or any other details.
If you read my response carefully, you'll see I'm telling him how to avoid using any wallet other than his own, and the P2P trader he's buying from. Not telling him to use the exchange, but to obtain direct contact with traders. That's how I got mine, the same guys I sell to from years ago. It's got its own risk, sure, but we all operate risking our reputations -- that's in some way a lot more secure than escrow.