I have issues with the Kilo-5 trilogy...
Well, I'd say the story begins at Halo 3.
Bungie knew they had to wrap up the trilogy's story, while still retaining a level of mystery in order to facilitate future Halo projects. As a result, a number of plot points in Halo 3 were intentionally left open. These are the most important points, in my opinion:
1. MC and Cortana drifting towards a Forerunner planet.
2. Mendicant Bias saying that he is sending John to the Forerunners.
3. The Gravemind promising that he would return.
I'll add a fourth and a fifth one from Ghosts of Onyx/Halo Evolutions:
4. Covenant splinters, but the forces present in their home territories continue to war against each other and the UNSC.
5. Halsey + others trapped in Onyx.
Bungie considered making Halo 4 at one point, and even made some concept art, but they later decided against it. Cue 343i and the inevitable release of Halo 4.
From a game design perspective, the Covenant are instrumental and an incredibly important part of a Halo campaign. It wouldn't be Halo without them. I think this is quite clear in Halo 3/ODST; remember how many people disliked the Brutes as enemies and hoped for the return of the Elites? I wasn't the only one!
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In order to facilitate Halo 4's campaign, back-story was needed. 343i needed to explain why:
1. The Covenant was at Requiem.
2. The UNSC was at Requiem.
3. Why is John fighting the Didact?
2 and 3 are not the issue here; they were handled by the Greg Bear trilogy and Halo 4 itself.
1. But.. the Covenant was "finished"? Indeed, and a splinter faction would need to be created.
As a result, 343i needed to justify why the Covenant was here in the first place, and why Jul still hated humans. Halo 3 gave us the impression that things were going generally well between Elites and humans.
And this is where my disagreement lies. Jul M'dama and his rebel faction were the product of ONI's incompetence; their insistence on targeting the very same species that played their part in preventing Truth from activating the rings.
I'm not sure whether 343i intentionally wanted to portray ONI as the space CIA with their signature screw ups, but I wasn't very happy with it. I feel that they could have approached the Covenant remnant without ONI involvement. It would make the UNSC seem less hypocritical, and I wouldn't be rooting for Jul in Spartan Ops as a result.
Secondly, the whole ordeal with Halsey. Do. Not. Want. It came out of nowhere, and it was completely unnecessary in the context of Halo 4's story, in my humble opinion. I feel that a lot of people have touched on this point already, so I won't say much more.
TLDR: A combination of the plot points of Halo 3 to ONI screw ups left me with an unsatisfied opinion on how the Covenant was brought into Halo 4.
I haven't even touched on how disappointed I am on Spartan Ops and Escalation, especially when compared to Halo 4's campaign, FuD and the Greg Bear trilogy. (The former are bad, the latter are fairly good to great).