Basically, give everyone the ability to do a background check and require them to keep a simple log of who they sold a firearm to (and proof of the background check) in the event it is later used in a crime?
That sounds pretty close to making all gun owners comply with FFL requirements.
On the rare occasions that I have sold a firearm, I have sold to gun shops, precisely because I did not want to sell a firearm to a stranger and not have confidence that it was going to a legal owner for legitimate purposes. But that is my personal standard. If I found a buyer of whom I had personal knowledge, should I not have had the ability to make that sale of my personal property?
I understand what you mean, though Skans - it is hard to argue against background checks to a public with 10-second attention spans.