Does a bike powered by a 1000w BBSHD? Probably not. That should be treated like a moped. Licenses shouldn't be required in places that are unwakable, and lack adequate public transport. But you certainly shouldnt be riding them in trails.
A 250-500w mid drive like the tsdz2? If kept at a lower gear I don't see why not. Especially for disabled or low-mobility riders.
Even then it matters less what you're running and more how much power you feed it, but people are assholes and will abuse anything you let them.
This 100%. And the trend is moving in this direction, if this news from a while back is any indication. There, the US Forest Service made the following conclusions for Tahoe National Forest:
Class 1 e-bikes are similar to traditional mountain bikes in terms of components, relative speeds and impacts to trails.
And:
The inclusion of Class 1 e-bikes as an approved use on the trail expands access to individuals that may not be able to walk or ride a traditional bicycle as far or long.