The main reason to fly high is to reduce air resistance. Air gets less dense at higher altitudes. This means the airplanes can fly faster and use less fuel. The same throttle settings give the same fuel consumption and might get the airplane up to 250 knots at sealevel but over 500 knots at cruise altitude. This means you get there in half the time and therefore burn fuel for half as long spending only half as much fuel.
Airplanes would have flown higher if it was not for the speed of sound. When you fly close to the speed of sound there are a lot of negative effects including higher air resistance. And flying higher and faster means you get closer to the speed of sound.
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