This is an interesting thought.

Do we know that most new software runs in batteries? Do you have a reference for that? It would be useful.

Other question is - does a sleeping CPU always win, or are other optimisations such as memory usage, screen usage, and communications, more important? I know for sure that the CPU is not the main consumer of power on a bunch of Android phones that were used in an academic study.

I don't have hard numbers. Most computation is probably done on servers. But power matters there as well (a lot). Most devices sold today are laptops and smart phones, I think. Some people claim that the IoT will be a thing real soon now, with embedded sensors everywhere.

Probably the CPU is not the main power sink on mobile devices (screen and radio are I think). But cranking up the optimization level is free for the developer.

So, this was my point - is it really free for the developer? For example, GPGPU compilers full of subtle bugs cost significant development time.

GPGPU is still relatively new and the tooling is still under work. But compiling with g++ -O2 instead of -O0 is pretty safe