I have been using f.lux for years and it has definitely had a huge impact on me. I don't have any scientific data to back up my claims, but f.lux is a fantastic product.
When you consider that f.lux released a side loading version of their app on iOS and then Apple threatened to remove their developer license, and then after it was pulled, released their own ripped off version of the software that does not work as well, you can understand how they might be upset about that. I understand that is business, but as someone who has used both I find f.lux to be completely superior.
Apple probably should have bought f.lux and then integrated it into their products, but instead decided to do it themselves. I'm not saying the software is earth shattering, but they spent years on the problem, and it feels as if Apple implemented their version in a few days.
I think Apple should open up the screen/display APIs on iOS to allow f.lux and other similar apps to be installed. I would happily pay for it rather than use night shift.