Most of us really wouldn’t mind if people who needed a little extra help (older people, injured people, people new to the sport) were riding bikes that provided a small assist to help out with the hills. It’s actually great to see older people being able to ride again with some help from a motor, for example.
But instead, we’re seeing a lot of e-bike builders abusing the concept to hack or build bikes that are basically electric motorcycles. It gets old fast when your local mountain bike trail is now crowded with kids motoring up the mountain on their modified e-bikes without even pretending to pedal. It’s even worse when they end up deep into trails they’re not qualified to ride with a dead battery and no natural ability to pedal back out.
The end result has been a blanket ban on e-bikes on most trails and a lot of animosity toward e-bikes. I wish there was a better compromise, but after watching all of the dumb outcomes play out on my local trails from a small handful of people abusing the concept, I understand why it had come to this.
I am pretty sure this is not currently true on almost all US National Forest land. Anything with a motor qualifies as for motor vehicle there and you will only be allowed on trails marked for motorized use on the MVUM maps. This includes mobility devices
Occasionally there will be someone waiting at the trailhead writing tickets to people who come off the trail with an e-bike or an off-leash dog. This seems to work as word spreads through Facebook groups and people stay away. Also generates some decent revenue when someone can write tickets for an hour and hand out a couple thousand dollars in fines for blatant violations (they stand right next to the very clear signage at the trailhead)
And the great bit is that if you are ignorant of these laws and get caught on an electric bike doing higher speeds then you get a penalty as if you are riding a motorbike without insurance or a license - aka penalty points on your regular driving license, plus all the other court shenanigans.
When I think electric motorcycle, I think of something that does not have pedals at all.
The US "class" system seems useful, inasmuch as it more or less specifies the capability of the bike with and without pedaling. I'm all for adding a new transportation / recreation option, and have adopted a wait-and-see attitude for how the technology and its use will evolve. So far, e-bikes have not affected my use of a conventional bike, except for people asking me when I'm going to get an e-bike.
The only next thing we saw was the Honda Spree, which as I recall had an electric starter and whatever qualified as an "automatic transmission," and I think that class of scooter is still more or less the standard today. It seemed like a big step forward in terms of ease of use.
As an example, https://en.wikipedia.org/wiki/Puch_Maxi
A used bike might fit your bill. Or the DIY route. The friction motor might be a bit iffy, but you might be able to buy an electric front or rear wheel for not too much and use the same electronics.
The Grin Technologies motor simulator https://ebikes.ca/tools/simulator.html predicts (the "Load Line") 837 Watts for "MTB upright", 648W for "MTB, Tuck" and 570W for "Road, Tuck".
I do find that in an upright position it takes 100-200W of human power in addition to 750W power measured at the input to the motor controller. The controller's pretty efficient, but the motor (GMAC) is only 85% max, so there's maybe 570W at the axle. The US CPSC and California laws aren't clear whether the 750W/1 horsepower limit is power in or power out, but power in is what shows on the display, so I limit it to that. Also, even a mild grade will cause the motor to approach the 70 deg C limit I chose after 1 minute. I live in the flattish Santa Clara County, but I'd definitely want a mid-drive if I lived in a hilly area. A 250 or 350W Riese & Müller Delite https://www.r-m.de/en-us/bikes/delite/ I test rode needed a lot of human power to hit the 45 kph max, but it climbed hills in Larkspur like a goat.
750W will have no problem getting a recumbent bike to 30MPH, but don't count on it for an upright.