I use f.lux, and it's great, but it doesn't affect brightness.
I don't want to turn down the brightness because then I've turned down the maximum brightness. My brightness tolerance runs on a curve - at one end, there's the brightness I'm okay with for the page as a whole; on the other end, there's the brightness that's okay for a single pixel, and they're nowhere near each other.
Logically, then, you should never use #FFF for large areas.
The actual problem is the lack of a brightness-controlled colorspace.