There are a lot of sound reasons to maintain constant speed (RPM). My favorite used to be the C-130 Hercules aircraft - considered by many to be the world's most successful cargo aircraft. During operation, the four turbojets run constant speed no matter what activity if performed. To adjust power output, the pitch of the blades is moderated, and fuel consumption rate is adjusted to present specific available power to the blades.
Four very strong engines on an airframe are very easy to coordinate. Vibration quotients throughout the craft are more stable, and the engine life is elongated through constant speed. Ancillary systems are tuned to that RPM, and the system is more efficient.
For as much as any power system may be "notched" into a specific portion of its power curve - never leaving that notch, constant RPM can serve as an endurance factor. By moderating fuel input & mixture (including turbo boost), cam timing, and torque transfer, very efficient operation is possible. If the notch is selected in the most favorable portion of the power curve for application, you can expect the maximum-available power at peak load, and moderate economy during light load. Idling is a loss factor, unless the controls 'step' from true idle to power.