The problem is one of speed differences and short sight lines on many sections of bike paths. If one comes around a bend and there are people standing in the path chatting then it becomes a matter of stopping distance. Same problem comes into play with joggers that traveling at half the speed of most people on a bicycle. If you crash into anyone it becomes a no win situation. The reality is that no law enforcement person is going to come and take photos and witness statements, contrary to the b.s. shown on televison. Riding any bicycle on a "bike" path is risky and one needs to be cautious when sight distances are limited. This is nothing new and even when Sacramento put in one of the first bike paths in the early 1970's this was a problem as there was high brush along the sides and people out walking or pushing strollers along the path.
The regulations restrict use of a motorized vehicle and I would bet that means a gas powered engine and not an electric motor with current laws. There are minimum horsepower regs to keep people on scooters off the freeways and there are federal regulations that vary by country (e-bikes are sold all around the world) that are supposed to require a speed governor to limit the top speed of an e-bike. There are open sections on a bike path near my house where I often ride my regular road bike at 30 mph on the flats and 50 mph down the hills. But I do not rely on my bike's brakes to get me out of trouble.
An e-bike for myself and my wife is only so we can haul 20 lbs of photo gear on a rear rack to get to locations. Otherwise even at age 71 we have no difficulty riding 40 miles over hilly terrain with our road bikes. I am looking forward to trying a e-bike with 3-4 inch wide tires on dirt trails as that is not something I would want to do under my own power alone.
It comes down to being one of those increasingly rare people that exhibit common sense and are courteous to others on the roadways, paths, and trails.