For the question "No hay muchas casas ________ el monte." meaning, there aren't many houses on the mountain, why wouldn't sobre work? If I wanted to say "there aren't many books on the table", wouldn't sobre be acceptable in that instance?
you could also say "en el monte" or "sobre el monte", but those will literally mean "on/on top of the mountain". The preposition "por" indicates an approximate location, as if "scattered on the mountain". I have added a hint indicating that we mean an "aproximate location" to be more clear. I hope this helps.
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