It would require companies to track serial numbers that go into the store, and serial numbers of items put on shelves, or otherwise legally leave the store. After a while, it'll be clear which items & serial numbers were legelly sold vs. stolen. And, to address the original point, copied stolen serial numbers still aren't any good.
The serial numbers of stolen items get reported to the authorities and/or Amazon, and it becomes their legal problem. As another post in this thread poins out, pawn shops have to do something similar to check for stolen items. So there is some sort of legal framework in place.
Im not saying that this should be i plemented or anything, I'm just trying to say that individual serial numbers might work. It will not be easy to implement, and cost money. But so does rampant theft. Maybe it's worth pursuing.