Dozer it's what a whole group of us do. Most Saturday mornings. It's enjoyable. The extra weight is a blast to throw around. Your arms will hate you.
You need to try it.
I've got no gripe with you guys taking to the trails and enjoying it, good for you. The point I'm pushing is that at no stage is it acceptable to ride that bike back up the trail.
Let me try another angle:
Most mountain bike trails are made to be ridden in one direction. This is accentuated by the shape of some of the features. For example, a downhill trail goes down and has features that are sheer faced (drops, rocks, logs etc) that have been built o the bike rolls off it in one direction and can't be ridden up. It's built like that for that reason; it's a directional trail. Now consider a loop style trail (cross country) where the features of that trail are far less consequential but are still shaped in one direction. Fair cop, you could ride the other way over or around those features but that's commonly done on trails that are marked or known as multi direction trails. In that instance, it'll contain some up's and down's and people ride to those conditions. At no stage should they be ridden at speeds that don't contain some anticipation that a person may be coming the other way, thats common sense and courtesy. You know those times you're bombing along and a moto rider comes around a blind corner impersonating his favorite metal mulisha hack and doesn't give a fuck for you on your mountain bike? Yeah, that's a big problem and isn't acceptable. The upside is you've probably heard the goon coming and know to give them a part of your thought to give them as much room as you expect them to give you...............
Now picture the same scenario with some dickbag on an E bike going all hero and showing off to his vespa riding buddies who rides his overweight lazy arse back up a single direction trail and doesn't anticipate that a rider coming down at a great speed cannot hear him and they have a collision. I can hands down guarantee you that if I was involved and could stand and see part ways straight that I would bend that bike in half by hand and crush the rider inside it for being such an arrogant dopey inconsiderate arsehole. That'd be the entree actually!
I build trails that stop people riding up them. Some brainiac moto riders have tried to come up some of my trails and failed but being the courteous guy I am, I hear them in advance and don't plow past them. I don't want to hit anyone and I don't want to have to repair trails that have been unruly damaged by someone not taking the obvious initiative that they are going against the grain. Der.
If you choose to E bike off road, stick to the trail direction and you should be fine.