Mountain bikes are a bit of an obsession of mine, though I've never used a bike with motor assist.

One problem likely to be encountered with military use is that the bicycle has limited adaptability to carrying weight, and troops these days carry a lot of that. A load on the rider's back is very unstable at speed and not healthy for the rider: a standing or walking position allows you to carry a load primarily on you hips; a natural cycling position does not, and any load on the back tends to put a lot of stress on the rider's lower back, especially on uneven terrain. The traditional solutions, panniers and handlebar bags, have limited capacity.

There would likely be some application for quick quiet movement over relatively friendly terrain with minimal load, but on a large scale, I don't know. I would be curious to see how much the US military could manage to spend on a bicycle, though!