All that said, I do agree the term is overloaded. The bike lines in NYC often have people riding electric mopeds in them and that feels dangerous. Their max speed is clearly way above 20mph and they’re bulky. They belong on the road with other mopeds. So IMO the definition of ebike should factor in max speed more than it should throttle vs not.
(And also, seconding the awesomeness of ebikes. My kids love riding on it and it’s allowed us to take so many trips that would have been difficult otherwise. It’s also allowed us to avoid buying a car, for now at least)