Question

Why are so many large optical telescopes located on mountaintops

Answer 1

Avoid cloud and man-made lights

Answer 2

Because light is degraded when it has to pass through air.

The best places for large telescopes would be on the Moon, in space,
or in orbit (like the Hubble, Kepler, and Webb space telescopes). 

If you can't manage any of those places, or can't afford them, then
the next best choice for a location is any place where the light doesn't
need to plow through a lot of air to reach your telescope.  Those places
are either on top of mountains or under giant helium balloons.  Both of
these ideas have been used extensively for the past 100 years.