You do realize e-bikes only go 25 km/h? You're confusing them with speed pedelecs. Those go around 50 km/h, although that's still a far cry from scooter speeds, let alone motorbikes.
In some European countries, yes, but other countries like the US have different laws. The UK doesn't have a classification for a speed pedelec, just the 25kph class.
What defines an "e-bike" varies from jurisdiction to jurisdiction. It also changes when talking in a colloquial context.
There are electric riding devices that are bicycle-shaped that go up to 45 mph (72 km/h) that are being sold as "e-bikes".
It's why it's hard to talk about e-bikes and regulation surrounding them because you can say "e-bike" and people think you're talking about entirely different things.
For example, in Oregon, for something to be an e-bike, it must be only pedal-assist and only up to 250 watts, which really will only take you to about 15-20 mph. If it has a throttle button so it doesn't require pedaling, then it's classified as an e-motorcycle, regardless of power rating, and so is licensed and registered like a motorcycle.
But enforcement is weak, and parents often don't know, so they'll buy their kids what is legally an e-motorcycle and they'll rip through neighborhoods at 45 mph, not even aware that their kids even riding one at all is illegal.
Where I live (western EU) it's simple. If the speed is limited to 25 km/h it's an e-bike. Above it's a speed pedelec and requires registration plate + insurance.
Just to be clear - it's not the speed that is limited, it's the assistance that is. You can still pedal above 25km/h on your ebike just fine and it's legal, but it has to stop giving you assistance above it(in contrast to say, mopeds, which have to be speed limited to 45kph).
Most US states allow 28 mph e-bikes. Some limit it to 20 mph. E-bike laws -- like all traffic laws in the US -- are set by the states. (as you may notice, even our cars do not have "united states" license plates)
The basic problem that causes laws like these to be passed is companies selling technically-legal "e-bikes" that are, in practice, electric mopeds you can remove the speed limiter and useless-but-technically-functional pedals from with fifteen minutes of work, converting them into illegal motorcycles.
