I have wondered that too, is bikes don't need front plates then cars should not either.
Public safety. They used to be mounted inline on the front mudguard and were mostly made of pressed metal. They were nicknamed "pedestrian cutters/slicers" (like pizza cutter/slicers). In the 70s they were declared "no longer required".
It would be possible to mount front plates on bikes across the forks. But then you'd have the mounting bracket and all it's associated protrusions now sticking out of the front of the bike as well, which would be no different to the pedestrian cutter only now it's a stabber.