This goes back to 1985 when I bought my Raleigh Olympian new, hopefully it's changed since then.
I purchased a bike registration for my new Raleigh Olympian, as I recall it was technically required, but later I found out that there was no sharing of information among police departments. If my bike were stolen and recovered in my city, it might do some good, but if it were recovered across the street in a different city it was worthless. Once I learned that I said never again.