As far as companies keeping fired bullets from firearms, a quick search didn’t find any evidence that it’s happening. Ruger says that some local jurisdictions keep fired casings, so they supply one with each firearm sold so the local dealer can send it to the appropriate bureaucrat.
As for being able to link fired bullets to individual guns, there’s a lot of wishful thinking involved. Here’s an article from Scientific American -
“courts have recently begun to recognize the scientific limitations of one forensic field: firearms identification, in which an examiner visually compares fired bullets or cartridge cases and opines on whether the items were fired by the same gun. Contrary to its popular reputation, firearms identification is a field built largely on smoke and mirrors.”
https://www.scientificamerican.com/article/the-field-of-firearms-forensics-is-flawed/
I like having a serial number on a firearm so I can prove it's mine if stolen, but I can see the argument that I should be allowed to remove it if I wanted.