You are of course correct.
I do believe developing such a system is possible however. Such as you mention with fingerprints to narrow the field down. You could use data points such as caliber, number of rifling grooves, direction of rifling twist.
But the number of variables that would enter the data set after the samples were taken when the gun is new would make the system only marginally useful.
As a barrel ages the rifling markings on the fired bullet changes due to barrel wear. Things like cleaning the gun, use of mechanical lead/brass removers, and the firing of hundreds of rounds through a barrel substantially changes the barrel’s imprint on a fired bullet.
Oh, gross mechanical features could narrow it down to a few hundred, or hundred thousand, guns of the same manufacture. And then you'd have to hope the bad guy had the gun "fingerprinted" first.
After being burglarized (guns were in a safe, my coin collection wasn't), I learned a lot (the hard way) from the police fingerprint tech as he dusted for prints. He said even human fingerprints ain't what TV and the movies have cracked it up to be. Breaking even a common case of burglary takes a lot of luck, even with fingerprints. "Ballistic fingerprinting" of guns would be a thousand times less effective than that.
All the billions that would be spent on "ballistic fingerprinting" (it deserves quotation marks, just like "smart guns") would have no measurable result, except as an excuse to collect guns, and not bother to return them.