An e-bike is just a bike from a traffic rule perspective. It is a bit noisier than a regular bike, goes about the same speed (in fact, the motor cuts out at about 15 mph). Its main advantages are that it helps with acceleration and with headwind/hills, but once you're at 15 mph you're on your own.

If you have a situation where dogs regularly interfere with bicycles and the other way around then I suspect that the problem is more with the dog owners (you?) than with the cyclists. I've been a dog owner for many years and my dogs have never been in a situation where cyclists would endanger it, though, I have to admit, one of my hounds once did endanger a cyclist by giving chase (pink spandex, not 100% the dogs fault, but then again they supposedly don't see color). I consider that wholly my fault, the dog pulled the leash right out of my hand and then refused to stop giving chase and that should have never happened.

It all sounds to me like you need something to be worked up about and you've decided that e-bikes are a menace to dogs when in fact the spaces where dogs are allowed to run free are not typically exclusive to dogs but are also shared by dogs with foot and cycle traffic. The responsibility for keeping the dogs and the other traffic safe lies squarely with the owner of the dog. A well mannered dog will stay with its owner and will not interfere with others on foot, bike or otherwise.

Finally, dogs are a much bigger danger to other pedestrians, and children in particular than your typical e-bike will ever be to a dog.