You are correct in understanding that airlines primarily fly higher in order to have a more efficient flight, as there is significantly less drag due to the thinning of the atmosphere.
However, there are a couple issues that grow as you raise your altitude. Your wings and engines are more efficient in providing lift and thrust respectively at lower altitudes. The wings create lift via the difference in air pressure going over and underneath the wings. When you increase your altitude, your wings become less efficient because while there is less drag, you now need to increase the speed of air passing your wings in order to retain the same pressures, which then produce the same lift.
Supersonic flight (flight over Mach 1) is significantly different than subsonic flight. The air will separate from the wing when it breaks the sound barrier, and will thus cause you to lose lift. As stated in the previous paragraph, as you increase your altitude you need to increase your speed. Then, as you approach Mach 1, drag increases exponentially. The average jetliner cruises at 0.75 mach, so you can see that we are already close enough for comfort to this barrier.
The engines themselves are also reliant on air passing through them to provide thrust, and will become less efficient at higher altitudes.
In short, it really becomes a balancing act, where you have to determine if the extra altitude, and speed, is worth the drastic increase in fuel needed to power the engines to get you to an appropriate speed for your altitude. With today's technology, it is not considered cost-effective.
For comparison, the supersonic "Concorde" jet topped out at roughly 60,000 feet, while the subsonic "747" jet tops out at roughly 45,000 feet.