Common sense wattage restrictions (I have seen 1hp or 750W as a threshold, for example, and apparently parts of Europe do 250W limits) are perfectly feasible.
Apparently federal law on imports dictates that the class of 'low-speed electric bicycles' is defined by a maximum of 750W and 20mph, which is a surprisingly appropriate envelope - about as much as you'd want out of a single-rider passenger bicycle with a heavy rider or cargo in a hilly city.
* https://en.wikipedia.org/wiki/Electric_bicycle_laws#Defined
That's part of the EU recommendation for classification as an assisted bicycle (pedelec) rather than an electric moped (e-bike): 250W maximum continuous rated power, assistance-only (user must be pedalling for engine to engage) and progressive cutoff to 25km/h[0] (so the cutoff starts earlier, at 25km/h or above there's no assistance)
[0] ~16mph
(This isn't a good thing. A poorly enforced law is a great vector for discrimination.)
http://www.dutchnews.nl/news/archives/2015/03/electric-bikes...
During my daily commute from and to work I think about one in ten I pass / pass me is an electric motor supported bike. It seems that mostly elderly people are riding them, but more and more people under 50 are using them as well.
Note that e-bikes here are normal bikes with an electric motor to assist the cyclist to keep a (slightly faster than) normal pace. Personally, I dislike the e-bikes who behave like mopeds/scooters and go 30km/h or more because they're dangerous. Especially on bike path given the difference in speed between regular cyclists and these electric monsters.
Then again everyone rides bicycles here.