The Covenant part is a very good point that I didn't think of. That should have been explained in the game for sure. However I still see nothing in those Forerunner books as required. I didn't even read them until after 4 and I knew exactly what was happening. The Librarian explains it to you as soon as you meet her.
The things you mentioned are not necessary at all to understand the plot. It's all back story. The Librarian explains that the Forerunners were leaving for their "Great Journey" and that Humanity was being left the mantle, she explains that the Didact opposed this and what the Composer is. She explains that Humanity was powerful enough to oppose them at one point.
Halo 4's plot itself was about the Didact wanting to use the composer to turn humanity into Prometheans. That was the plot, and she tells you all you need to know to understand that. I would agree that a game shouldn't rely on other mediums to understand it's story and with the exception of the Covenant which I didn't consider before, I don't think Halo 4 does that at all.
https://www.youtube.com/watch?v=o-4r_5AE6D4
Once again, I simply disagree with the notion that the terminals aren't a valid way of telling part of the story. Especially when it is all back story.
As far as the Cortana thing, she was written very differently yes, and it's totally fine to not like the direction they took it in, but Chief was actually the one insisting that they would fix her while Cortana throughout the game is trying to basically tell him to let her go, with a couple of scenes here and there where she expresses sadness and fear about dying. In that situation, she seems like the stronger one to me. She even saves him at the end.
Also Chief was always special, even in the fall of reach he was exceptional. And Bungie's own trilogy certainly paints him as special.
It seems like people's biggest issues are the fact that these characters are different now. 343 clearly wanted to humanize them and it's certainly not up to me to tell anyone how they should feel about the result. You're welcome to your opinions.
I never said Halo 4 was exceptionally written or anything. I do think it was solid and did a very good job of telling a focused story. Bungie's scripts were all over the place and littered with holes.