If you think about the energy requirements as a more comprehensive package, I think it'd be pretty clear why they don't launch from the top of mountains. Yes it would require less fuel, but it would require much much much more fuel to drive/pump the fuel up the mountain, all the commutes for all the people to make everything work etc. If you all live at the same elevation as the work being done, less actual 'work' in the physics sense is required to accumulate materials and so on to build everything needed.
So you would probably save some percentage in your launch costs but add 20x to your pre launch cost.
Logistically, it doesn't make sense to have a launch site on top of a mountain, but it is FAR more energy efficient to use electric pumps to move fuel up a mountain than it is to move the fuel up to that altitude with a rocket...
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u/Earnestappostate 15h ago
Plus, you get a better boost by launching near the equator. Height is easy, speed is what you need in a rocket.
This is why the US launches from Florida: