I'm not entirely sure how it would be possible to make any secure conclusions about the provenance of a gun that was used in a crime. As far as I know, it is not legal to keep a registry of serial numbers and who they were originally sold to. Moreover, in most states, you can sell firearms privately, without any background checks or paperwork at all. I have only purchased one of my firearms in an actual gun shop - the half dozen others are inherited, or purchased from friends, family, or randos on Craigslist or Uncle Henry's. Good luck tracking back the chain of custody on some of those...
This isn't really workable. One of the primary ways criminal gangs acquire firearms here in the US is through "straw purchases", where they have someone with a clean record go purchase a gun for them.
This works fairly well for them, but has its limits: if guns you've purchased later turn up in crimes, you're likely to face pointed questions. You can't do this too often without putting yourself at serious risk.
But straw purchases of ammunition are almost impossible to track. If the buyer is asked to account for their ammunition, they can simply claim to have shot it all already.
Meanwhile, it adds great expense to ammunition (My local stores mark up their ammo nearly 100% already, and it will become worse next January once it's illegal for me to order ammunition online). And because criminals actually use very little ammunition, this cost falls almost entirely on legitimate target shooters and hunters, who are the ones shooting tens of thousands of rounds a year.