Another reason why ammo serialization is a bad idea:

Sample ammo serialization bill, Section 5 paragraph 3 –

Any person who willfully destroys, obliterates, or otherwise renders unreadable, the
serialization required pursuant to this bill, on any bullet or assembled ammunition is
punishable by imprisonment not to exceed one year, and a fine of $1,000.

(Taken from ammunitionaccountability.org, set up by Ammo Coding Systems to promote the ammo serialization bills)

Considering the damage that can be done to a bullet, and consequently the serial number, when it hits an object, anyone firing a bullet risks unlawfully destroying, obliterating, or otherwise rendering unreadable the
serialization on said bullet. This goes along with a lot of other bans that may not have that as the original intent, but there is always a risk it could be used that way in the future.