That has already been addressed.
Driving a motor vehicle on a public highway is a privilege. With that privilege comes conditions, obligations. Firearm ownership, bearing arms is a constitutionally protected right. Apples and oranges. If you are going to justify abridging the right to firearm ownership you have to go apples to apples , pick another right, such as felons can't vote. Even at that, abridging that right requires an extraordinary circumstance. Barring an extraordinary circumstance as it pertains to gun ownership, we're back to abridging a constitutionally protected right.
Also, the background check has verbage/questions, punishable by law if a false answer is given. Do you plan to sell the firearm, are you purchasing the firearm for resale or the transfer of ownership.
I'm not necessarily a hardliner. However, I am uncomfortable with the notion of getting something passed, make it palatable so at least something gets passed. At least that would be progress. Progress suggests and is indicative of movement towards a destination, a goal. Incremental steps, each step used to justify the next. Precedent. To what end? We've seen it, "The Founders did not envision extending the right of gun ownership to weapons of war, such as a cannon", which is false. No, the government taketh as the government can taketh, incrementally if necessary, by design. Call it progress or sort of shady dishonesty towards an intent, an ultimate goal of abridging a constitutionally protected right.