E-bikes are cool.. use them where permitted to use anything motorized and you're good.. i have no problem with them as long as they are used properly and in accordance with the law we all have to follow ..
Problem is like @Reelamin
said "most" are getting them to go where they shouldn't Legally because they dont give a frick about anyone else but themselves. and when doing so are in clear violation of the law.
A lot off topic but, On the topic of "it should all be foot traffic only no horses cuzz they suck and tear up so much ground" .. hate to be the bearer of bad news but 999,999% of all trails in the united states where put in and are where maintained by horses accessing them. When was the last time you hiked 37 miles into the frank church to clear trails with a hand saw???!!! I'll wait!
without them your beloved foot traffic only trails would be slim to none! And the next time I'm on my trusty steed and I see a hiker/hunter benefitting and following the maintained trail that has been put there and maintained by horse traffic, I'll stop and ask .. sure is nice having this trail here isn't it?? and I will bet .. I know their answer.