Requiring background checks for private gun sales sounds like a good idea until you do the research on the effort vs benefit. The effort to enforce this would be massive and virtually no gun crimes are committed with these guns anyways. In practical terms you'd have to track every firearm and figure out what to do when Grandpa does and leaves his gun to his children. A parent would have to run a background check on their own child of they buy a gun for them as a gift. Realistically, the only time it could be determined that a gun was sold in private without a background check is if the gun is eventually used in a crime and recovered. The vast, vast majority of guns that wind up in the hands of criminals are through corrupt licensed dealers and straw purchases.

If the purpose of gun control laws is to prevent violent crime, then there's no loophole here since this is not a significant source of weapons used in violent crimes.