Interesting thought you have there.
Wouldn't it be in the best interest of law enforcement, and the citizenry, to have those serial numbers made public? What would be the downside?
Say for instance, that I buy a gun online from a person I don't know. It gets shipped to my FFL, we run the serial number, and the gun is hot. We contact the seller, as well as the police, and they proceed to track down the bad guys and return the property to the person who got robbed.
You would get your money back, and the person who did not check the serial number to see if it was hot is up the creek, unless he can get in touch with the person that he aquired it from and get his money back from them.
In reality, I don't think that police manpower is up to tracking these things down, unless there was a task force within the BATFE that was responsible for doing this exclusively.
The only downside I see to this, would be them asking for a registry of ALL firearms, so they would have a comparison list. They wouldn't need one, but they would most likely push for one anyway.
WG840