I think you are failing to understand:
"Attenuated S4" means you get less S4 sleep (the kind you need).
Please read it again. It was the high 6700K color temperature (i.e. not f.lux) that reduced good sleep, while the 3000K color temperature (e.g. f.lux) increased good sleep. This means f.lux is good for sleep.
"not statistically significant" -- removing the blue did nothing useful -- "exposure to the computer monitor only was reduced slightly relative to the dark control condition" -- the computer monitor putting out the blue light was the same as not having the thing on at all: blocking the blue did nothing useful.
Granted that it wasn't statistically significant, perhaps due to a small sample size, but the measured effect was in the direction of f.lux (blocking blue light) being good for sleep. They emphatically did not find that f.lux was bad for sleep.
" lower color temperature bright light exposure during a night rest break led to a reduction of subjects' arousal level during the subsequent work." -- you have to intentionally get up in the *middle* of a sleep cycle for there to be any effect; prior to a sleep cycle, there was no effect. This is basically "If you wake up in the middle of the night, you are less alert the next day". That's a big "duh".
You are misunderstanding the experiment. The subjects worked from 11pm to midnight, then took a break from midnight to 1am, then worked again from 1am to 2am. Being exposed to f.lux-like light during the hour break made them sleepier. So yes, obviously, f.lux is bad for staying awake if you're trying to stay awake. But the direct implication is that f.lux is good for going to sleep if you're trying to go to sleep. So again, f.lux is good (for its intended purpose, which is to use it before sleep).