FWIW, there is a mechanism currently in place with NICS for private sales. A gun buyer and a gun seller can go into any FFL's premises and request a private sale background check. The buyer fills out a 4473 as usual, and the FFL performs the check. If the buyer gets a "proceed", the gun is transferred and either the buyer or seller pays the transfer fee to the FFL. If the seller is "denied", naturally the transfer cannot legally take place. It is not a perfect system, but it is there should a seller have concerns about who is attempting to buy his/her weapon.
I couldn't rightly give this a 'like' because the FFL is much more involved and placed in a potentially dangerous position. Something serious is being overlooked or simply disregarded. Every transfer an FFL accomplishes has to be recorded in his A&D (Acquisitions and Dispositions) book. If the sale doesn't go through either because the transferee failed to pass or the sale was simply canceled, the dealer cannot simply pass the gun back to the owner. A form 4473 and background check must be completed and approved before the gun can be returned to the original owner and logged out of the A&D book with the NICS transaction number or code. If the seller doesn't pass the background check, the FFL dealer is left holding a gun he doesn't rightly own, cannot return it to its owner, and put in danger of life and limb of the obviously dangerous individual who wants his gun back and who's record of felonious or mentally unstable background caused him not to pass.
As an FFL, I will not place myself in such a position.
Woody