I think you underestimate the power of a digital database. Sort by make, then sort by serial number, and you see the history of each firearm, at least where there are “universal background checks” (the liberal’s dream - for this exact reason). Also, grandpa’s gun from 30 years ago will still be on the list, if he never sold it.
What we need are criminal penalties for violating the law about not compiling a gun registration database. But, no chance of that happening during the Brandon administration.