I'm not trying to nitpick, but there is no private sale loophole. It's not a flaw in the law, but the way the law was purposely written. It was intended to exempt the occasional private sale from the background check requirement because it was felt that requiring one would put an unfair burden on the individual to involve an FFL dealer in the sale and pay those associated fees.
So, it wasn't a mistake. It was a carefully worked out compromise between pro and anti-gun folks that helped get the background check law passed. And it's very far from a universal belief that it needs to be done away with. Not all of us believe we need the government to hold our hands, or that the occasional sale by a private individual to another private individual is a problem. Innocent until found guilty via due process, remember? It's an essential, fundamental concept vital to a free society.
And it happens be be a perfect example of that darn slippery slope anti-gunners think we are silly for worrying about. The gun owners of America are constantly lied to that if we just agree to the next step of "reasonable" gun control that it will solve the problem of gun violence and we'll be left alone. Just one more law. We all know that's a lie because attacking the low hanging fruit of legal gun owners in an attempt for a magic bullet fix (pun totally intended) at the expense of our constitutional rights never works.
I, again, point out that the MOTIVATION of those who commit violent gun crimes is the real problem we need to solve. We've got plenty of laws already on the books and a perfectly fine background check system in place, if we would just dedicated sufficient resources to implement them correctly.
At least that's how I see it.