That is already how it is set up in Europe.

Regular e-bikes have to have their electric assist limited to 25 km/h, but you can still pedal faster than that on your own power.
If an e-bike is not limited to 25 km/h, then it falls in the category of speed pedelec, which requires a licence plate and insurance.

However, it is trivially easy to illegally remove the limit on some models of e-bike, and many people (mostly teenagers) do remove that limit. They then recklessly cycle at excessive speeds down the bike path, without regard of other cyclists who may be cycling there.

The issue in the Netherlands (idk about other place in Europe?) is lack of enforcement of the existing rules against tuning e-bikes.

Edit: Also worth noting that this is by no means a new problem.

We used to have the exact same problem with people tuning their mopeds, back when blue-plated mopeds (which are also supposed to be limited to 25 km/h) did not yet have a helmet requirement. After helmets were made obligatory a few years ago, most of these people moved to e-bikes instead.