I'm pretty sure the issue for f.lux being removed wasn't them telling people to install - it was that their "container" app could download and execute an arbitrary IPA file. The reason being is that the f.lux source code is not open source, so they didn't want to distribute that. Instead the container is able to execute arbitrary IPA files, meaning that some could use it to pirate apps.
You can do that anyway. Their "container", as you call it, is just an Xcode project that uses your own code signing cert to sign a precompiled binary. There's nothing magic about that. Xcode does the exact same thing every time you build a project from source. The only thing they did was make it slightly easier by removing the need to run the commands by hand in Terminal.
It was removed because Apple said that distributing an iOS app outside of the App Store without using enterprise app distribution violates the developer program agreement, which means they can't distribute the unsigned, compiled binary in the first place.
On mac, f.lux provides an extra option to change the color temperature settings on the basis of apps. For instance, while running Quicktime one can disable f.lux. To do the same in iOS would require f.lux to know what apps are running and track them. Its against iOS privacy policy.
Only since iOS 9 has Apple actually prevented apps from getting a list of running processes. And IMO, this is just one example of why that change was a bad idea, though there are certainly examples of why the change was a good idea. Another example is VPN provider apps, who benefitted from knowing what apps users were running, to help them determine how best to prioritize testing of apps while the VPN is connected. So IMO, this is another case where certain apps should have an exception from those rules, simply because the rules interfere with legitimate behavior (as opposed to ad frameworks checking for other apps en masse for dubious purposes).
Except in this case, f.lux for iOS never existed (outside the jailbreak community) in the App Store. They can't even claim to be ousted by Apple, because Apple never let them in in the first place. As long as Night Shift isn't announced for OS X, Apple is not even in competition with f.lux. All there is, are demands to break the App Store rules, because the f.lux duo claims to have good intentions regarding chronobiology.
You are technically correct—the best kind of correct. However, f.lux originally had a scheme where if users signed up for a free developer program membership, they could grab a pre-compiled binary of the app and run a script to sign it themselves for their own, personal devices. Apple forced them to stop doing that, effectively relegating the tool to the jailbreak community, whereas before, users could use it without jailbreaking their devices. IMO, that's some serious overreach on Apple's part, despite the fact that their licensing terms do technically give Apple the right to make such demands.
This is yet another reason that we desperately need a usable set of third-party developer tools for OS X and iOS. No company should have that much control over what products can and cannot be made available to their users.
Also, remember Apple put that API call in, which means that this was in development before flux. People generally don't just put random APIs in for no reason.
Considering that f.lux has been running on iOS for five years in the jailbreak community, you're trying to tell me that Apple has been developing this minor feature for five years? As others have pointed out, the APIs in question are used by other parts of the OS for various color management reasons. I doubt Apple management even considered this feature until they got so much backlash from the user community for telling f.lux to stop distributing unsigned binaries for end users to sign themselves.
With enough continued public backlash, they might even relent and grant f.lux permission to use the SPI officially. It certainly can't hurt to try.