The pedals on a motorised bicycle must be the primary source of power for the vehicle. If the motor is the primary source of power then the device cannot be classed as a motorised bicycle. For example, a device where the rider can twist a throttle and complete a journey using motor power only without using the pedals, would not be classed as a motorised bicycle.
If a car is at fault in an accident with a bicycle or ebike, their motor vehicle insurance will likely cover your cost for repair and hopefully medical expenses. But what happens if you are at fault, riding an ebike illegally because you did not register it as a Moped? At best, you could be prosecuted under the law. At worst, you could be financially liable for neglect or reckless endangerment via a law suit.
In a friction drive motor, a small, solid wheel rotates against the side of the tire in order to drive it. The first motorcycles used the same concept, with a motor mounted above the front wheel. The problem is that the drive rubs at the side of the tire. It's inefficient, and it quickly wears the sidewall away. Tires need to be replaced every couple hundred miles. For this reason, you'll seldom see electric bikes with this type of drive anymore.
The federal Consumer Product Safety Act defines a "low speed electric bicycle" as a two or three wheeled vehicle with fully operable pedals, a top speed when powered solely by the motor under 20 mph (32 km/h) and an electric motor that produces less than 750 W (1.01 hp). The Act authorizes the Consumer Product Safety Commission to protect people who ride low-speed electric vehicles by issuing necessary safety regulations. The rules for e-bikes on public roads, sidewalks, and pathways are under state jurisdiction, and vary.