I’m a bicyclist and I think this is not a bad idea. Class 3 e-bikes have engines which can accelerate to a top speed of nearly 50 km/h which makes them practically slow motorcycles at that point. A collision between a pedestrian and an e-bike accelerated to top speed will send at least one person to the hospital. And the risk of cyclists who blatantly flaunt traffic laws is also present, even though most people in my city tend to follow the law. There’s a bike path in my city which is used as both a commuter route and a recreational route, and some people ride their e-bikes at crazy speeds just centimetres away from children riding their tricycles.
What I wouldn’t support is the extra paperwork burden. Opponents of this law are right when they say that it should be made easier to switch from driving to using an e-bike, not harder. But minimal registration formalities are probably fine, as long as they are made relatively easy. Maybe something like a registration plate which is affixed at the factory and which you have to register using the DMV website or an app. This would also make tracking down stolen bikes easier.
Governments don’t hate privacy intrinsically. They just don’t think it’s important. Violating privacy using mass surveillance has no visible downside to the uninformed public. Policy makers just notice that destroying privacy makes it easier to catch cybercriminals and decide it’s a worthwhile trade off. You probably disagree with that. But there are far too many people who just go along with it.