You can still get a citation on a bicycle. If you are biking at night with no lights, you get fined. You can also get a DUI on a bike. There are other laws, but they are rarely enforced.
I think it’s just too much to keep track of. They keep track of mopeds, and boats with motors over a certain size. Dogs have to have rabies tags, proving that they have been vaccinated. People are supposed to have at least an ID card, after a certain age.
Should bikes have plates? I don’t think so. They’re too plentiful, and the parts are too interchangeable. Whenever I used to have a couple bikes that don’t work, I would make a working one out of the parts. I guess that’s done with cars too, but they have VIN numbers on certain parts, to keep track of the main components. Most bicycles have a number on the frame, but it is rarely used for anything other than identification of the bikes in a store setting.
Bikes get stolen SO much, that they’re almost interchangeable in urban areas.
We have bicycle rental stations in my city. They require a payment card to be rented. I assume that those bikes have a tracking number of some kind.
I wouldn’t care much for having to have a plate on a bicycle. Too much of a hassle.