If putting serial numbers on bullets is a good idea to help solve crimes involving guns wouldn’t it also be a good idea to put them on prescription pills to track down whoever is supplying those who abuse those drugs? Or how about serial numbers on cigarettes to help prevent cigarettes from getting into the hands of underage smokers? Or tracking the serial numbers on paper money to combat the recreational drug trade?
The answer is no to all these ideas. Anyone that suggests serial numbers on bullets is as stupid and/or ignorant as someone who suggests serial numbers be tracked on the other items.