I'm sorry, but going 35mph in a bike lane/path is irresponsible and dangerous. If one has an ebike capable of that sustained speed then one should just drive in an auto lane, like a scooter. The whole point of creating those bike lanes was to give bicyclists a safe place to go at human-powered types of speeds without the threat of getting overtaken by powered vehicles going at much higher speeds. IMHO. The reason that these paths & lines prohibit powered vehicles like scooters is not because of some inherent bias against petrol engines, but because their higher speeds prompt safety concerns.
For anyone out there that currently does this, or is thinking about getting a bike that can do it in the future, please reconsider. This thread is full of people reporting that ebikes are currently being tolerated even on paths that have signage ostensibly prohibiting them. I suspect it is because the vast majority of people have class II bikes and are traveling at speeds that many human-powered bikes already go, so it hasn't created any issues. But if enough cowboys go out there traveling at speeds equal to or higher than even cars can go on residential streets, it's only a matter of time before they ruin it for the rest of us. You are right that the current regulations are virtually possible to enforce. But where I think you are wrong is assuming this means regulations will just be removed completely. More likely, if & when this ever becomes a pressing issue, the impossibility of enforcing class II will be "solved" by going the other way: just completely banning ebikes without exception on some paths (that is easy to enforce!)