the more i think about this whole debate, the stranger - and stupider - it is.
16 CFR 1512 has long had a definition of "bicycle" for the purposes of establishing safety requirements around such vehicles. for example, they are required to have brakes; either rear only or front and rear. there are lots of other basic safety requirements, all falling under the federal hazardous substance act regulations. if a "bicycle" doesn't comply with these things, it's hazardous and not legal for sale or use in some context in the United States. "any bicycle offered for sale to consumers in disassembled or partially assembled condition shall meet these requirements..."
nowhere in the federal hazardous substance act, or part 1512 in particular (i actually read the whole thing!) does it say that a state, county, or city MUST allow bicycles anywhere at all. a very, very clear example of this is that many states permit riding bicycles on sidewalks, some do not, and most grant counties or cities the authority to forbid it. california, as a state, allows it, but san francisco as a city, does not. alabama, as a state, forbids it completely.
nobody rational has ever claimed that because the federal hazardous substance act defines what a "bicycle" is that it must be allowed to be ridden on sidewalks. or roads. or interstate highways. those three things are public infrastructure constructed and maintained by different jurisdictions which are each allowed to make their own decisions about safe use.
the addition of the low speed electric bicycle to 16 CFR 1512 does not change the ability of a state or county or city to limit the use of bicycles (or electric bicycles).
let's set all the curiously american questions about jurisdiction aside and look at it more practically. the federal definition doesn't specify any speed cutoff, only a maximum power for the motor ("less than 750 watts") and a maximum speed achievable through use of the motor alone ("maximum speed on a paved level surface, when powered solely by such a motor while ridden by an operator who weighs 170 pounds, is less than 20 mph."). practically speaking, this means the motor is limited to between 175 and 300 watts in a steady state at 20mph. (300w for MTB tires, 205lb total load, upright seating position, 175w for road tires and riding on the drops.) let's just call it 300w.
cruising at 15mph, a bike under this definition has the same limits as a "class 1" ebike, which is also limited to 750w, and allowed to provide 750w of assist up to 20mph. the bike, on it's own power alone with the ride ghost pedaling, could take you up a 10% grade at 15mph. no difference at all between class 1 and "federal" bike. ditto flat ground at 19.5mph. you can ghost pedal and go 19.5mph on either bike.
it gets SLIGHTLY more interesting above 20mph. let's say i want to go 23mph. on a class 1 ebike, i have to do all that work myself: 415 watts for the upright position on the MTB tires, beyond the capability of most casual riders. the "federal" bike would continue to help me out with 300w and i have to supply 115, no problem. so i can go a little faster, but ONLY the amount faster that my own legs are capable of providing. a typical casual cyclist, not trying to get all sweaty is probably limited to around 150w, so we're talking about the difference between 300w and 450w. how much faster is that? ABOUT THREE POINT FIVE MILES PER HOUR. 450w gets you about 23.5mph. the federal bike gives us a whopping 3.5 additional miles per hour!
not too exciting. if only there was a definition which allowed MORE. oh wait - there is. the "class 3" ebike allows 750w of power to be delivered up to 28mph. i can now ghost pedal and go 28mph, which is meaningfully faster than 20mph. so, assuming you're a casual cyclist willing to put down around 150w while riding around town, it can be summarized like this:
class 1 eBike: 20mph max
federal eBike: 23.5mph max
class 3 eBike: 28mph max
i think the whole debate would be different if there was some federal law that said "all cities, counties and states must allow anything defined by federal regulations as a bicycle to be used anywhere." but there is no such law. and there never ever will be. why? the constitution. "The powers not delegated to the United States by the Constitution, nor prohibited by it to the states, are reserved to the states respectively, or to the people."