The big issue is that of the actual search.
OK, there's been a shooting. Forensic scientists have recovered cases from the scene, and even a couple of expended bullets.
Now what?
Somebody has to go through a gigantic file of cartridge cases and sample expended bullets, looking for a match with the samples retrieved from the crime scene.
It's pretty easy (comparatively speaking) to search for similar fingerprints, essentially a two-dimensional artifact with well-defined characteristics.
But cartridge cases and bullets are not only three dimensional, but could be, in a metaphorical sense, four- or five-dimensional, with tremendous variation in every characteristic, in terms of making close, accurate comparisons.
Computer programs exist to compare fingerprints with a huge database, but those programs can search based upon well-defined single characteristics.
I am skeptical that a viable, usable computer program can be written, which will compare the myriad variables in each and every characteristic of the possible markings on cases and bullets.
It might be a matter of time: We can do a search which will return accurate results, but, because of the great number of variables in each characteristic, that search may take years to make an accurate, individual match. Maybe centuries.
Collecting cases and sample bullets is merely another example of the fact that it's easier for a government to inconvenience law abiding citizens, than it is to actually catch, prosecute, and punish criminals.