Because it would make it a lot easier to stop them. At a gun show, a guy who goes from show to show selling guns at each of them and making a business of it looks no different than a guy who just inherited his dad’s personal collection and wants to liquidate them.
Because it would be a lot more obvious to everyone who’s breaking the law. If someone offers you a gun without a background check, you’ll immediately know it’s illegal. No one will offer them openly on facebook. Purchasing the gun would mean you also committed a crime, so many people would be afraid to buy guns from people offering them without a background check because you don’t know if it’s a sting. (or they might rat you out later)
It doesn’t.