Checkboard,
Well said. The reason why airliner jet engines are more efficient at high rpm is because they are designed that way, where the rpm and the temperature rise together. The blade area, speeds and airfoils are all designed as a delicate balance between the needs of burning little fuel in high altitude cruise and the need to crawl away from a takeoff at high power at low altitude.
The basic efficiency of an engine is determined by how hot it can get internally. The higher its heat, relative to the temp around it, the more efficient it is. That is because any heat engine must allow its heat to escape to the outside, and the greater the temperature difference between the two places (combustion chamber and outside) the more easily the heat does work as it gets out.
If you simply plot the fuel needed to perfrom one horsepower, it will drop as the combuster temperature rises. That is why engine research is devoted to new ways to cool and new materials to withstand the heat. Maximum permitted temperature is the story of engine efficiency.
The rpm of a jet engine is locked with its temperature only when you set all those blade design parameters to be that way. You can make the blades quite efficient at any rpm, it is not high rpm that makes efficiency, per se, it is the engine matching that drives temperature and rpm up at the same time, in cruise, that allows the peak cruise efficiency to be reached as peak temperature is reached. In other words, it is temperature that makes efficiency in any engine.