Mostly because it's nice to have an uninhabited area downrange of the pad.
The benefit of launching from altitude would not be the potential energy, but the lower air pressure and density. The first would enable rocket engines to operate at higher expansion ratio, and the second would reduce aerodynamic forces. The benefit is apparently not large enough to justify the difficulty of operating on a mountain.
The goal of the rocket is to get the payload high enough to be in space AND fast enough to be in orbit. It's the later that takes most of the fuel, IIUC.
I can imagine two different answers to that and depending on which one you tend to think more there are two different answers to your question.
If you are thinking: space is high up therefore the higher we start the easier we will get there.
The problem with this is that getting into outer space is not that hard, staying there is the hard bit. The international space station orbits about 408km away from the surface of the earth. That is not a long distance. If you would have a car which can travel the same speed a car can usually travel but straight up you could reach that altitude in about 4 hour easy driving.
What is important is what would happen after you reach that elevation and turn off the engine of your car. If you have seen astronauts serenly drifting in space, you might expect that your imaginary car would do the same. But that is not what would happen. You would see that your car starts falling and rapidly!
In fact there is a word for such a flight path. It is called a suborbital space flight. Space flight because it went to space, but “sub” orbital because it lacked something to stay in orbit.
What is that something it lacked? Why do the astronauts float gracefully while your car plumets? The trick is that the astronauts plumet too! They are constantly falling back towards earth, they just go so fast sideways that the earth rolls out from under them. In fact that is what an orbit is. You are falling around the earth with a very high sideways speed.
In essence staying in space equals being in orbit which further equals going very fast.
So now you can see that being high is not the hard bit of staying in space. Flying as fast as a bullet is the hard bit, and of course starting from high won’t help with that.
But! You might think a different thing why launching from a high elevation might help. Maybe you already know that staying in space == going fast. So you are thinking: what hinders us from going fast? The drag of our atmosphere! If we would launch from high there would be less atmosphere around us, thus there would be less drag, thus we wouldn’t waste so much energy to fight it. And you would be right! If you could launch from a high elevation you could spare some energy because there the atmosphere is thinner. But when you run the numbers you see that this is a very small percentage of your total energy expenditure. Mostly because our rockets fly through the dense part of our atmosphere relatively quickly wasting only a little energy to fight drag. Launching from a high elevation would come with it’s own set of challenges of course and wouldn’t help that much relatively.
So depending on which thing you were thinking about you have an answer. Hope it explained the problem better. If you have any more questions about any of the details let me know and I will try my best to explain.
Also sorry for answering this long a seemingly simple question. Would love to answer shorter, but you know it is “rocket science”. ;)
> If you could launch from a high elevation you could spare some energy because there the atmosphere is thinner.
Reminds me of Eve on Kerbal Space Program. Gravity so high and atmosphere so thick that I had to use a helicopter contraption to lift the spacecraft to the highest possible altitude in order to get the rocket to even make it to space to say nothing of the absurd delta-V needed to actually inject into orbit.
My guys were stuck on that planet for a long time...
My thought was that the first mile up would be the hardest to get through because of being closest to the Earth's center. And isn't it something like 1% of the distance that they need to reach for "cheap" horizontal acceleration?
The benefit of launching from altitude would not be the potential energy, but the lower air pressure and density. The first would enable rocket engines to operate at higher expansion ratio, and the second would reduce aerodynamic forces. The benefit is apparently not large enough to justify the difficulty of operating on a mountain.