You might be thinking of the Canadian pistol registration system.
I think that they claim it was used to solve one violent crime in the last 70 years, but some dispute even that one.
Registration has virtually no usefulness in fighting crime. It is certainly not cost effective.
Yes, I think you’re right about that, and that one wasn’t a ballistic registration program but names and serial numbers. Even viewed from a statist perspective or at least their publicly stated objecives, it’s a bad deal. When you factor in the loss of liberty and privacy to the people, it’s indefensible.