A database of shell case markings could be useful in identifying the make and model of a particular weapon (e.g. determining the shell casing was fired by a 9mm Bereta verses a different type of 9mm pistol) but I suspect it'll be a lot less useful for identifying the specific weapon out of millions on the streets. The shell case markings are less distinctive than human fingerprints, so you'll probably end up with a lot of duplicates and near duplicates, as pointed out in this blog and by this one.

There's also the fact that this would only work for new firearms purchased through ordinary means. Unless you require all of the 100 million+ firearms in the country to be ballistic fingerprinted, the database would be incomplete. It'd be like what happens when the police find fingerprints at a crime scene but they don't match any of the existing ones in the database.

As you pointed out, firearms that are smuggled into the country or that belong to criminals wouldn't be fingerprinted, either. Criminals, by definition, don't obey the law, so they wouldn't get their guns fingerprinted even if ordered to by the law. Ballistic fingerprinting would also be easily defeated by normal wear and tear as well as by deliberate tampering to the weapon which would change the markings.