A few other reasons that power use can be important:
*form factor (lowering cooling requirements can facilitate a lighter, smaller, and/or less exposed system; this is a factor with servers where data center space costs money as well as consumer electronics and deeply embedded systems)
*product cost (larger heat sinks add cost, fans add cost--material (including inventory) and assembly--, heat management adds design cost)
*reliability (keeping temperatures down reduces soft errors and hard failures, in addition power saving techniques like DVFS can also increase MTTF by reducing electromigration et al.; removal of active cooling can remove a point of failure--particularly one with a moving part--, even reducing active cooling requirements can improve resilience; tighter integration facilitated by lower power can also reduce vulnerability to mechanical stresses and external electromagnetic interference)
*performance (when performance is limited by TDP, energy-efficiency can increase performance; in addition, if the number of external connections (pins) for power and ground can be reduced, more pins can be available for signals increasing available signal bandwidth; lower power can also facilitate tighter integration which can improve latency and bandwidth)
There is also a distinction between chemical batteries and other power sources. Energy harvesting techniques and radioisotope power cells have different constraints than chemical batteries.
I realize that including all of the above in the introduction would have added too much length, but it is easy to forget how multifaceted power concerns are.
Replay available now: A handful of emerging network technologies are competing to be the preferred wide-area connection for the Internet of Things. All claim lower costs and power use than cellular but none have wide deployment yet. Listen in as proponents of leading contenders make their case to be the metro or national IoT network of the future. Rick Merritt, EE Times Silicon Valley Bureau Chief, moderators this discussion. Join in and ask his guests questions.