I am all for scooter style e-bikes to be allowed everywhere a bicycle is allowed including bike paths.
The only exception would be congested pedestrian paths with kids and dogs. Then I will conceed that no bicycles of any kind be allowed on those paths. I have no problem on paths with people myself and slow down accordingly. Everyone in my area knows me and I have never had a problem. Still there are nuts flying by on regular bicycles. So it goes back to, the problem lies within the rider of the bike, regardless whether it has a battery or not. I can safely cruise at 5 km per hour and enjoy my ride on the path, and speed up when no one around...A little common sense goes a long way regardless whether it is pedal driven or battery.