"e-Bike" is a clever marketing term for an Electric Moped. e-Whatever sounds modern and environmentally good. XXX-Bike reminds us it's just a bike, so no need for burdensome insurance or licensing.
I just spent a year in NYC where the restaurant food delivery business uses heavy throttle controlled electric-mopeds on the streets and sidewalks. More dangerous than bicycles because of their combined speed and weight.
I've done some bicycle trail advocacy and I fear that putting e-bikes under the umbrella of all bicycles will make it harder argue for trail access in areas deemed sensitive by the Sierra Club and similar groups.