I’m not going to get overly technical here, but consider this:
1. A study in 2003 estimated that the number of guns owned by civilians in the United States is between 238 million and 276 million.
2. The database required to house the number of individual pieces of information required for this to be effective would be horrendously complex in design, and require an enormous number of trained IT professionals to maintain (not to mention design, cost to license, and deploy).
3. The logistical enormity of the task.

Every single firearm in existence would be required to have (at minimum) the firing pin and breech face replaced to become “legal”. Every time you replace a firing pin (I’ve broken a few in my time), the database would have to be updated, and forget just being able to buy one, you’ll have to get it through a licensed FFL, and pay another fee for the update.

Not to mention that over time these “micro engravings” would simply wear off (any metal on metal contact will eventually remove enough material to render the micro stamping useless, this is why ballistics is not an exact science. The markings on a bullet fired from a gun at the factory will be FAR different than those of a gun that has had 50,000 rounds of ammunition run through it.

Bottom line, as you mentioned, in theory this may be a good idea (I’m not convinced), in practice it will have only bad effects. I really don’t think we need to worry about something like this as it is pretty much logistically impossible to do.