Why are many jet aircraft designed to cruise around FL350-370?
In a word, the tropopause.

Gas turbine engine efficiency improves with colder &amp; denser air. As an airplane climbs through the troposphere, the density &amp; temperature both drop, and the loss of density is more than offset by the lower temperature. Above the tropopause, however, the density continues to drop while the temperature holds (approximately) constant.

In the U.S. Standard Atmosphere model, this occurs at 36,089 feet. This represents a local (possibly global) optimum altitude for efficiency (and if there is a better optimum at a higher altitude, it's inaccessible for other reasons).