Yet another issue is that bullets aren’t as stringently controlled as the guns themselves. Even if you correctly identified the person who bought the bullets, his defense is going to be, “someone must have stolen a bullet from me last time I was at the range”, or “I threw those bullets out a year ago. I have no idea how someone else got them” or “I bought them, but I didn’t kill anyone. Maybe there was a paperwork error at the gun shop?”
Since no one is about to open a box of bullets and hand-read serial numbers at the time of sale, there WILL be record-keeping errors. Bullets will get put in the wrong boxes. Boxes will be mis-labeled. No doubt there will be numerous other ways for the data to get screwed up.
Given all that, it doesn’t seem likely that a serial number match to a purchaser would stand up in court. It’s not at all the same as matching a bullet to a specific gun, which is in the posession of the accused.
So at most, the bullet match will probably only rise to the level of probable cause to justify a search warrant. So for this to work, we have to assume that A) the perp is stupid enough to shoot someone with a tagged bullet he personally purchased, B) The bullet is recovered and the serial number read, C) The crime is unsolved, D) the bullet match leads to a search warrant which uncovers more incriminating information.
And how much per year are people going to have to pay for this dubious benefit?
C) above is important as well. The type of crime where someone might shoot someone else with a tagged bullet would be your typical crime of passion - a fight breaks out and devolves into a shooting because a gun is handy. But do these types of crimes typically go unsolved anyway? Very few domestic murders go unsolved. Usually the killer is in custody almost immediately. Most unsolved murders are things like drive-bys, liquor store shootings, contract killings, or other murders by hardened criminals, and they are exactly the kinds of crimes that are least likely to involve tagged bullets anyway.
And as Mr. Moto pointed out, there are billions of rounds already in circulation. Are you going to require them all to be turned in? Most people who keep a gun for defensive use still have the bullets they bought when they purchased the gun, and 20 years from now they’ll still have those same bullets. Right now, I have about 1200 rounds of ammunition in the house, and not a single one was purchased in the last five years.