These things should be registered like any other motorized vehicle and have a license plate.
Punish the crime of running people down, not of people wanting an alternative form of transport.
I think NYC law here is seriously misguided
Ebikes (limited to 20 mph) aren't usually the fastest bikes on the road
Anecdotally, I am a reasonably fast commuter cyclist and have been passed by ebikes many times. I have overtaken an ebike exactly never.
My experience is as an ebike rider on a long flat bike trail; while I did pass 90%+, I also couldn't keep up with many serious cyclists.
I still think NYC's push to keep them outlawed is ridiculous and counterproductive.
Also, I'm dubious that the purported problem is a big enough problem to society that it outweighs the benefit (healthier populace, reduced traffic, reduce pollution).
Do you plate requirements also apply to rollerbladers? They go at least as fast, don't even have brakes, and are much more likely to be found up on the sidewalk than any electric bike will ever be (sidewalks are annoying, they're full of these obstacles called pedestrians - much better to ride on the road where the obstacles move faster than you for the most part).
All I knew was that it was a blue sports car with a white dude, probably a Camaro. But a bystander was able to jot down most of the license plate, and the police found the guy. Because it was an accident, my parents health insurance wouldn't cover the ER visit, but the guy's auto insurance company did.
If this happened to you today, and you were hit by an unregistered vehicle, it's far more likely that the operator will get away. There's no license plate, and it's much more difficult for the cops to find a bike than a car. And there's no insurance, so accident liability is a bigger issue as well.
As you pointed out, you need to draw the line somewhere, I'm not sure where that line lies.