There's many ways to get around any laws against record keeping. They can make state agencies keep the records. They can get a private contractor to keep possession of the records. You can get a private organization to keep the records for free (I'm sure there are a few who would be glad to volunteer). And in all cases federal agents would have the privilege of querying the data.
Prohibitions are also worthless unless they specify criminal and civil penalties for violations, so that violators can be charged and also privately sued.
You've laid out the case against ANY type of background check. Bravo! I've been arguing for a good while that even "common sense" background checks shouldn't be allowed to stand as they infringe on the 2nd. People think I'm crazy, but all it takes to strip your rights to own a gun is to make you a felon (they control that), find out you're mental in some way (obama care) and you're SOL. No person should have to pass a government test to act upon their Constitutionally guaranteed rights.