If you have reasonable eyesight then there are a lot of advantages to binoculars.
As well as giving depth perception from the stereo effect, the brain processes the images from both eyes and gets much more information this way. This is particularly obvious in low light.
Its interesting to try binoculars in poor light, try closing one eye at a time, I think you will find the monocular view is much poorer. You may also discover that one eye has better low light and colour performance than the other. In my case its the none-dominant one. So for me a monocular would be no good, and the way the brain combines the binocular images gives me much better sight in low light. I had never noticed this before, until I took up stalking.
In woodland stalking the glasses should be heavily used. Nevermind eyestrain, the much better performance of the binos is worth the extra weight.
For the hill the glasses are used less, and the light is usually better, hence the traditional telescope (or modern spotting scope) can be more useful for the extra magnification. Perhaps a suitable monocular might do instead.
If you only have good use from one eye then of course the monocular makes good sense. They used to be popular a long time ago when any binoculars were relatively extremely expensive, perhaps unaffordable, but thats no longer the situation.