They use the serial number as a means to identify that you are actually the owner. Denver has a system where if you register you bike with the city and your bike is found they'll notify you.
The serial number sticker on my Specialized de-laminated and peeled off after a few years of commuting in occasionally damp conditions. I was kind of shocked that there wouldn't be a better way of uniquely identifying it if I needed to, aside from having pictures of scratches and dings.
For a more expensive bike it’s worth considering an active tracker.
Some guys near hear burgled a bike shop recently, and were busted quickly one of the reasons being the owners noticed the stock moving.
you can inset a label into the resin, or a metal plate with an engraving on it. Or engrave any of the other embedded metal parts already in the frame for connection with the outside world.
Yes, this is a solvable problem. My hunch is that there’s no incentive for bike manufacturers to deal with this. If there were permanent serial numbers that could be attributed to the owner, they’d have to respond to thousands of requests for verification.
It's worth doing a few things on the frame to make it unique. Bit of paint and so on. It both makes it identifiable and less attractive to professional thieves who want to flip whole bikes.
How hard is it to just publish the list of "found" and imponded bikes, that everyone can see?