A national firearm registration should be a positive thing, i.e., an inventory of who has what firearms, as part of a nationwide effort to keep firearms out of the hands of felons and the mentally impaired. Unfortunately, that ain't gonna' happen and can't happen, because as has been mentioned, there are real life examples where governments have used such registrations to seize citizens' firearms. So the concern is not just a hypothetical.
I think what would contribute to a reduction in gun violence is universal nationwide background checks on all firearm transactions, including private sales. And I add that last bit as one who opposed WA's initiative that created and closed the private sale loophole. The background database needs to be national, not state, so that people in Illinois can no longer drive over to Indiana and make straw purchases of firearms with no checks and then take them back into Illinois to sell illegally.
The other thing that would likely contribute to a reduction in gun violence is if mental health professionals were not only allowed, but required, to share information about unstable patients with local LE. But that can't happen due to patient confidentiality laws, and the advocates of those laws would rather seize everbody's firearms than make exceptions to that confidentiality. So essentially choosing patient privacy over public safety is to choose murder and mass shootings in some cases, cuz seizing everyone's firearms to keep them out of the hands of the mentally impaired ain't gonna' happen either.
The upshot is that Americans have chosen gun violence as an acceptable price of less restrictive firearm ownership.