E-bikes already have these in classes 1, 2, and 3. Everything else is not classified as an electric bicycle.

They already do this. Or - the law doesn't impose regulations on manufacturers, but it applies different laws to different classifications of vehicle, which are defined by metrics like top speed. So if a manufacturer wants their product to fit in one classification or another, they must put on speed limiters. Or at least, this is the way the law works in some places, and these laws are fairly standard, as they have been promoted by ebike advocacy groups for years who feared exactly the sort of heavy-handed regulation we are seeing in this post.

There are, unfortunately, a few problems.

First is public education. Most people buying any of these products don't know which classification they are buying, nor that the classifications exist at all, or that different laws apply to different classifications. Governments should take on the responsibility of informing the public about their potential purchases, and sellers should be required to clearly display a vehicles classification when selling in so consumers can make an informed choice.

Second is aftermarket modifications. While this will almost certainly remain the domain of niche hobbyists, the government should make it clear that if you do modify your vehicle, then it will be considered as part of a new class if it meets those standards and will have to follow those laws.

Third is infrastructure. Infrastructure for different classifications should be built differently to accomodate its preferred classification and exclude others. We already know how to do this with cars, and we can apply the same techniques to high-powered emotos.

Yeah, speed limits seem like a reasonable way to catch people who are not in compliance. If a bike is going faster than 30mph, and that's in a bike lane or on a trail instead of on a road, or they don't have a license plate, that could be cause to pull someone over. It is tricky because the 28mph limit for class 3 ebikes (in the US) is an assisted limit, and a strong cyclist might be able to go faster than that pedaling unassisted.

20km/h is the assisted limit in Europe (I think), but that limit is too low for a bike lane speed limit. Plenty of unassisted cyclists go over 30km/h.

People complying with the law already have speed limiters built into the bikes. But yes, it's a method to spot misbehavers.

The creator of the Youtube channel Berm Peak suggested that unregulated ebikes should not be allowed to have throttles, which would eliminate class 2 ebikes. That would make it much easier to spot problem riders, because they typically use a throttle instead of pedaling. That's also how Europe regulates ebikes (I think). You'd want some way for people with accessibility needs to get an exemption. I've heard throttles are nice for getting started from a stop, especially with a heavy load, or going uphill. But I've noticed that California law already makes a distinction between a throttle and a "start assist", and maybe a start assist could cover that use case.