OK, you tell me. How can we differentiate a 'motorized bike' from a 'moped' or 'motor scooter' or even a 'motorbike'? Now, it is intuitive that there is a difference, but there has to be some sort of definite, objective criterion--otherwise some leather-clad greaser on his Harley-Davidson can claim that he's just riding a 'motorized bicycle'.
Now, one may argue that the local governments' definitions are 'off', or too restrictive, but that there has to be some 'bright line' should be obvious.