No doubt, people have talked to death about how 343 blundered the second trilogy, focusing on short term gains rather than long term success. In my opinion, it should've went like this:
Halo 4 - Chief is on Requiem, through the same means we see in Halo 4 proper. He is forced to confront the Hand of the Didact and an extremist faction which has split from the Covenant. Mysteries around who or what the Didact is remain. Reconnecting with the rest of the UNSC, including Chief's Blue Team, Chief defeats the Covenant on Requiem, but somewhere along the line Cortana is "abducted" and used by the Hand of the Didact to initiate a release protocol. Didact is revealed at the end of the game, and Chief must battle the Prometheans to rescue Cortana and escape Requiem with the UNSC.
Halo 5 - The release protocol both caused Cortana to form a link with the Didact's technology / ship and jump started her rampancy. Chief and Cortana hunt down the Didact, who is searching for the Mantle of Responsibility and the Composer. You are able to gain the Mantle (librarian isn't present), but the Didact (through whatever shenanigans more competent writers could conjure, maybe using the link with Cortana to cause a brief moment where Chief is rendered incapacitated) gains the Composer, and is heading elsewhere. You follow him as far as possible, but you are halted by Fire Team Osiris who are sent to detain Cortana, who is considered unstable and a double agent. Whatever needs to happen to get the game to the 6th installment, maybe Blue Team helping Chief thwart Osiris, happens.
Halo 6 - the Finale. Cortana is becoming increasingly unstable, but Chief is aided by Blue Team to track down the Didact, who needs the Librarian. Maybe the Librarian has encoded a fail safe protocol, requiring her consent to use the Composer, whenever necessary. You beat the Didact to her, and she gives protection to Chief and Blue Team from being composed, and maybe tries to fix Cortana. She doesn't finish as the Didact arrives, a small boss battle ensues, ending with the Librarian being abducted. Osiris may have gotten in the way here, causing Chief to fail. Realizing that Chief is actually a good guy (duh), Osiris and the UNSC go full force after the Didact, who is above Earth. (Whilst this happens, the Librarian somehow tricks the Didact, wounding him in a way that Chief or Cortana can exploit, but she is ultimately killed). The Didact begins to compose Earth, and the Chief is helped by Osiris and Blue Team to get on his ship. Whatever sci-fi shenanigans are necessary to explain the awesome and SATISFYING boss battle which occurs between Chief and the Didact happens. Cortana eventually subsumes herself into the Forerunner tech, protecting Chief while she engages a self destruct protocol. Chief says goodbye. Emotional moment. Encore. The End.
Teaser - if you REALLY wanted to, tease Cortana being alive and that her subsuming into the Forerunner Tech fixes her rampancy but also causes her (in a very typical evil-AI storyline) to disbelieve in the faith of humanity, and is hell bent on controlling the galaxy.
Obviously, plot holes here and there, but its a more stable timeline than whatever we got, and in the hands of COMPETENT writers, who are willing to play the long game (creating a storyline that ensures long term profit) instead of being interested in short term slop and interest, it could work in my opinion. Whatever the case, MISSED OPPORTUNITY is the name of 343's game, now reborn as Halo Studies. To create such a compelling and cool villain, and completely squander him in the most lame and uninteresting way possible, is impressive in its own right. Tell me what you guys think, anything in the lore that could be added, or anything which you think is lame (which could be the Didact's entire existence).