Mopeds are step-through primarily to allow room for the engine under the footrest or above the rear wheel. For the same reason they have small tires and relatively high rake angles. In a lot of ways that's a straight downgrade: it makes the handling much less stable (which is why rake must be high), it makes the frame weaker (so it is constructed heavily to compensate) and it makes ride quality worse.

Electric motors and batteries have very flexible envelopes so you can fit a very powerful powertrain in a bike with no problem- the battery just has to be very skinny. The big wheels and responsive handling mean slow speeds are very controllable compared to a moped, and the handling and bike weight is much lighter.

What I think is really needed is an e-bike that is meant to be an actual road vehicle, IMO specifically that has a lot in common with a motorycle. Something with a much larger battery, streamlined wheels, a headlight and turn signals, and a comfortable seat. That would be just lovely. I still strongly feel that having a scooter form factor is not necessary to have those things, though. For instance the Haibike Xduro Trekking Pro[1] managed 32 mph and claims 30 miles range, but that's with pedaling (the bike provides 275% boost power). It also has front and rear lights, but no turn signals. Pretty good 51 lbs,and the frame looks like it's extra low to facilitate picking it up. Still, I wasn't able to find anything that provides the weight/power/range of an e-bike with the features of a motorcycle.

[1]: Warning, spammy subscribe popups: http://electricbikeblog.com/haibike-xduro-trekking-pro-2015-...

Maybe an e-dirt bike. Based on your preference of the ride of a bike over scooter, a dirt bike may be what you are looking for. The ones I have seen are built for actual tracks and off-road, but they might make some street legal versions or certainly you could install the light features and other equipment required to comply with your specific state law as many do with traditional gas powered dirt bikes.

Edit: I probably should have mentioned cost as the e-dirt bikes are not really in the same range as any scooter or e-bike I've come across.

> Mopeds are step-through primarily to allow room for the engine under the footrest or above the rear wheel.

Surely you meant the other way around?

Engines are generally too wide to fit between your knees, since an engine is usually a vaguely cubic shape. In early mopeds the engine was below your feet[1], so there was no point in having a crossmember where your knees would be.

[1]: https://en.wikipedia.org/wiki/File:ZweiRadMuseumNSU_Hildebra...

Aren't they simply step through because that's more comfortable for casual rides?

With motorcycles, and many mopeds for that matter, they seem to be able to put the engine between the legs.