I think many of us would be happy to ride an electric bike not least because we would gain access to all those lovely bridleways and the Restricted Byways NERCA cheated us of. Range aside, those which resemble conventional trail bikes feature motors whose power exceeds what is permitted on BW or RB while those with less power that are, are little more than bicycles and I for one have never really got on with narrow tyres in the dirt.
Perhaps this, seen on Preston Green yesterday, provides a reasonable compromise:
I wasn't able to talk to the man but Googling 'ON ONE' reveals it's a hand-made, non-electric mountain bike <here> so the electric kit will have been added afterwards.
Altogether a very nice concept that may appeal to the trail rider for the "quiet exploration of our rich heritage of unsurfaced byways" - the Enduro enthusiast may prefer to look elsewhere though!
I had a good look at electric bikes recently for pretty much the reasons you describe, there is some pretty interesting technology out there and range now is far less of an issue. Unfortunately cost is another matter, you could get a pretty nice used trail bike for the cost of a decently kitted out electric bicycle.
If you are inclined toward that sort of thing look at the "gruber assist" motors, they are a really slim electric motor that fits inside the tube the saddle slides into, which propels the bottom bracket (the pedals are connected to) from inside. They don't totally power the bike but rather take all/most of the hard work out of it, and let you keep up a good pace without being super fit.
These things are so hidden within the frame tubes, and run so silently that there have been some serious accusations of riders using them in competitive cycling events