Rockets require cryogenic fuels, workers and large launch complexes. In contrast, Everest is a mere 9km and the first stage of a rocket will take it to something along the lines of 100km at 2000m/s. It is much easier just to throw more fuel in the first stage (or move to the equator) than try and relocate around the relatively smooth surface of Earth.
Florida's air is humid and dense. You get lots of heat gain from that. The density itself matters. Condensation is a huge source of heat. Freezing is another huge source of heat. So you boil off cryogenics and maybe worse. We lost a space shuttle due to a chunk of ice hitting the wing. Falcon 9 rockets need unusually cold filler; if it warms then it expands and won't even fit in the rocket. It probably pours out and gets drained away, the alternative being a rupture.
The USA would do better launching from near Tuscon, Arizona. It's decently high up and dry, which helps keep the cryogenic content cold. We used to do this in fact, before the Mexican embassy complained about defective rockets crashing in Mexico. We chose to move to Florida instead of making a liability payment deal with Mexico.
I think it's mainly that the difficulty of building infrastructure up there, and hauling rockets and payloads up every time you launch, isn't worth the benefits. If you could magick a launch pad and rocket to the top of Mount Everest and launch it from there, you'd get a small but decent performance improvement.
I imagine it's a mix of mountainous terrain making it hard to transport launch vehicles to the top and most mountains aren't next to the sea (so the payload would have to travel over land, raising the stakes of an unplanned early failure).
Those are not mutually exclusive, you could build one on some plateau in the andes near the equator. But I guess the economics still don't work out for that.
> Dumb question: why don't they launch rockets from the tops of mountains?
Not a dumb question at all. It would actually give you some non-trivial advantage - but altitude matters considerably less than speed when trying to achieve orbit.
Starting a mile higher would allow you to avoid the densest parts of atmosphere, giving you less air resistance and helping with the Max Q, or maximum dynamic pressure (rockets sometimes need to reduce their engine output until they have cleared the denser atmospheric layers, or they would break up due to air resistance stresses).
This does unfortunately not outweigh the cost and complication of moving your launch site on top of a mountain. If you're really after every scrap of advantage, moving your launch site closer to the equator is way better than moving it up (until you already have it at the equator, that is).
The low pressure lets them get away with toroidal tanks, pressure fed booster engines, and a relatively large faring. Or at least that's the plan, they haven't launched anything close to orbital class yet.
The point isn't to get higher up, the point is to get out of the damn atmosphere so you can use wider bells, lower chamber pressure, and lighter weight tankage.
Because doing stuff from the tops of mountains is very difficult. The logistical complexity and cost of doing something from the top of a mountain swamp out the comparatively small advantages.
Also, the best places to launch from are near the equator where there is a large body of water Eastward. And there are very few mountains in such spots.
Altitude is much less important than velocity.* The extra altitude you'd get from launching from a top of a mountain would not be worth the expense of having to lug the rocket up there in the first place.
Every time you get some altitude, you also get a minuscule amount of velocity because the Earth is rotating. A space elevator gets you so much mind blowing altitude that you'll also get all the velocity you need.
