I agree that's not the same thing as a statewide or nationwide "registration", but it does connect the gun to me
connect the gun to you, but certain steps have to be followed, and only on that particular gun.
Under the current system, if a Glock 19, serial #ABC123 shows up at a crime scene, the ATF can issue a trace request. They'll find that Glock shipped it to Tactical Ninja Gun Supply on January 4th, 2007. They'll call TNGS, who will inform them that they shipped the gun to Joe Bob's Tackle and Gun Shop on January 29th, 2007. The ATF then contacts Joe Bob and asks him to pull the 4473 for that specific gun. Joe Bob goes through his records and finds that he sold it to Bob Periwinkle on February 3rd.
That's the current system. Registration is different. Under a registration scheme, all of Bob Periwinkle's guns would be in a central database, under which an agency could simply pull up his name and find everything he owns.
The current system makes any sort of confiscation scheme very unworkable. A central registry would make it child's play.