I think you and other people are overthinking it. Just post speed limits. Jogging trails should probably have 10-20 mph speed limits, depending on the width, and bike trails maybe 25-30 mph. I can easily get a single speed up to 20 mph on a straight away, no electric assist. Downhill, I can get it a hell of a lot faster. Considering most aren't geared properly to really allow pedal assist at top speeds, most electric bikes are about the same as a normal bike. Maybe a bit faster. Once you get over a kilowatt, you're starting to get into motorcycle territory, and they should be limited in speed while on bike trails.
They aren't motorcycles though, so they shouldn't be outright banned. They're the same size as normal bikes and don't produce any fumes. For the handicapped, they might even be the only option for prolonged bike rides.