This has been on my Mac for a long time, it's a program called f.lux , a big YAWN if this is all that 9.3 has. boring.
For one thing, I find taking away the blue light really cuts down on visibility of the screen. It's not so great to be squinting hard at the screen. I often am disabling it. Better to turn off and go to bed.
Some people don't have the self control lol, or have specific reasons related to work and such to be using their devices later in the evening. The less harsh light is less.. Harsh. Makes it easier to go to sleep after putting the device away rather than feeling wide awake because it was bright as day. This feature isn't meant to be used in the day or bright environments, because yes, it would cut down on visibility then.
Almost looks like a leaked image for an iPad with 3D Touch...
ALSO - I have to say that I'm loving Night Shift - for kicks I turned it off on night in bed and the sudden change to the bright cool screen made my eyes tear up from the brightness.
Yep, I never realized how awfully harsh these screens were until I did the same as you.
Why would you turn it on for just one evening? This feature seems to be something that you generally would want to remain active unless you turn it off temporarily while watching a movie, for example.
I've found on a few occasions that I was in a darker environment, needing night shift, before the timer I had set for it was ready to shift the screen automatically. Or other times where it was the opposite and I needed more regular colors. Good to have a quick option.
If light is the cause of insomnia, would it be hard to put that ipad away for few hours and sleep? Where did you get this research from?
Again, some people don't have the self control, or have important reasons to be on their devices in the later hours of the day, like work or such. Anyway, this is what I have heard scientifically about the feature; we have a circadian rhythm which is related to the day/night cycle and sleeping. Something like seeing all the blue light after hours tricks your body into thinking it's still day, so less melatonin is released, so you aren't tired. The yellowing follows the sunset which corresponds with a proper circadian rhythm. The dimming/yellowing of the screen begins the release of metaltonin well before you go to bed, so you are tired when you are supposed to be. Your internal clock is correct in thinking it is night. This all theoretically equals better sleep.
No specific source but this is what I have heard a lot of.
Might've been just a placebo but first time I got Night Shift going, it was like 7PM. I already began to feel drowsy while using my device, where that typically doesn't even occur for another couple hours at least after a long day.
... I have been waiting and waiting for them to give us "dark mode" for night time!!! ...And to fix issues with Maps not going into night mode fast enough, or having to close it and reopen it to get it to switch, want a manual toggle for this...AND make all of Maps go into night mode, not just when you start turn by turn directions! 
