"Longer battery life" can be restated as: a lower ambient temperature for your room/office; less CPU cooler fan noise; a lower power bill; the ability to pack more servers per rack in a co-lo environment (yes, servers run browsers–headless ones, for spidering/scraping); etc. It can even be restated in terms of extra performance, when you consider technologies like Intel's Turbo Boost.

Even if power use is a minor concern for desktops, it would be good to program with energy consumption in mind :>

Network utilization, CPU usage, memory, disk usage, energy consumption. Lots to focus on...

I would expect that lower power use is highly correlated to low CPU/GPU use, which can be beneficial for other reasons than reducing power use.