Motor-driven cycles may be operated on the roadway without registration, but the operator must have a driver's license.[85] The cycle may not be operated on any sidewalk, limited access highway or turnpike. If the maximum speed of the cycle is less than the speed limit of the road, the cycle must operate in the right hand lane available for traffic or upon a usable shoulder on the right side of the road unless the operator is making a left turn.
Hmm, that’s unfortunate. I actually have a doctors note that I carry along which recommends the use of an assisted bicycle. I ride thoughtfully and have never been asked to show it. I cannot comment on the federal parks, perhaps they are not aware of the federal law classifying electric assist bikes that perform at or below 20 mph and 750 watts as bicycles. Having a note and this information would be a good response if you were questioned.
The Ohio Revised Code 4511.01 [121] distinguishes motorized bicycles and mopeds from motorcycles or scooters by describing them as "...any vehicle having either two tandem wheels or one wheel in the front and two wheels in the rear, that is capable of being pedaled and is equipped with a helper motor of not more than fifty cubic centimeters piston displacement that produces no more than one brake horsepower and is capable of propelling the vehicle at a speed of no greater than twenty miles per hour on a level surface." One brake horsepower converts to 0.75 kW, or (rounded) 750W. Thus, a bicycle with an electric helper motor operating under 750W, and not propelling the bicycle over 20 mph, does not qualify to be registered under Ohio state law. Local jurisdictions may have other regulations.

In Quebec power-assisted bicycles are often classified similarly to standard pedal bicycles. They do not have to meet the conditions defined within the Canadian Motor Vehicle Safety Regulations (they are not classed as "motor vehicles"), but they do have to comply with federal regulations that define Power Assisted Bicycles. The Quebec Highway Safety Code defines a power-assisted bicycle as a bicycle with an electric motor. PABs are permitted on the road in the province of Quebec.
Again, these are base level components here. The Shimano/TX55 gearing is fine for this application level but I have lost my chain a few times in a few weeks. The frame is surprisingly solid aluminum alloy which feels stiffer and lighter than last year’s Ancheer. The supplied front 10W light is very bright, however the back light is charged via USB and has a push button rather than being wired into the controller. The disc brakes are the same no-name brand as the Ancheer but appear to be a size bigger. The fork, while not amazing, is a big improvement in stiffness and give over the Ancheer’s, which scared me a bit.
Haibike ships the HardNine with 29-inch tires, 180-millimeter hydraulic disc brakes, a 100-millimeter front suspension fork, and a nine-speed Shimano shifting system. The bike’s LCD readout is affixed to the handlebars and displays the current speed, level of charge, remaining range, and current pedal assist mode. The company says the battery can be completely recharged in just four hours, minimizing downtime between rides.