I think this is part of a wider problem with Halo's storytelling that's been with the series from the beginning: the disconnect between the games and the books. 343 made it one of their priorities to try to close this gap, and the results have been mixed. Bungie made very few serious attempts to resolve the disconnect, instead choosing to ignore or take from the books at their convenience. Reach is the best example of this: they wanted to tell a story that didn't involve the Master Chief, so they ignored The Fall of Reach instead of trying to work around it. In my opinion this lead to a better product, but for people who really enjoyed The Fall of Reach I can see why the annoyance kicked in. On the flip side, we have 5 which introduced Blue Team without much explanation at all. They weren't mentioned in any previous game and existed solely in the books. Halo 3 makes it seem like MC is the last Spartan and really runs with him as a sort of messiah for humanity. 4 doesn't do anything to dispel the notion that he is the only Spartan II, so 5 comes along and drops Blue Team and moves on like nothing happened. It was jarring, and that's where the red flags should have started going off in our heads (when we learned Blue Team would feature in 5) because 5 jumped the shark in more ways that just Blue Team.
I tend to be in the camp of "Halo 4 was good standalone and didn't require knowledge from the books", but knowledge from the books certainly helped a lot. 5 is exceptionally jarring without at least having read The Fall of Reach. The rest of the story's failures have nothing to do with it being too tied to the books, but BT's existence is a big one.
So the question is: did Bungie make the right decision to mostly ignore the books? I think so. Contact Harvest, Halo 3's dialogue, Halo 3's terminals, and I Love Bees all contradicted one another with regards to the relationship between the Forerunners and Humans, so we can't just blame Microsoft for making life harder on Bungie since those 4 things all came from Bungie itself. It really comes down to whether or not the Nylund-verse should have been given more serious treatment in Halo 2 and 3. I don't think we'll ever be able to answer that definitively, but I think that Halo 3's story benefits greatly from Master Chief being the lone Spartan II.
Here's the back of the box blurb from Halo 3:
The Covenant controls Earth, the all-consuming Flood is unleashed and the fate of the galaxy hangs in the balance. An ancient secret, buried under the sands of Africa for untold millenia may hold the key to our salvation or our doom. Spartan-117, the Master Chief, a biologically augmented super-soldier, must uncover that secret and stop the forces that threaten us once and for all. He is the last of his kind, a warrior born for combat, bred for war... and humanity's only hope.
Now imagine the last sentence starting with "He is one of the last of his kind". Not so romantic and biblical anymore. You are the Master Chief, the last of your kind, humanity's last hope. The buck stops with you. That's empowering, and it's one of the reasons why 3's story, despite its flaws upon closer inspection, is so effective. The premise is so darn compelling that the execution didn't need to be perfect for the story to feel perfect. When you muddle the premise with "well, actually, he's not the only Spartan II left", you take away a very powerful and compelling tool out of your toolbox. 4 was headed in a fascinating direction, setting up 5 to explore Chief's relationship with his own humanity and isolation. 5 ditched that entirely and did, well, whatever the heck it was that it did.
People have been clamoring for the games to include more from The Forerunner Saga (my favorite Halo books), so much so that it seemed like a unanimous opinion around here that 5 would feature Mendicant Bias. We were all completely wrong. With 5, 343i took the most fruitless parts from the books and ignored the most fruitful parts, IMO. 4 took the fruitful parts and was all the better for it. 3 had a closer relationship with the books but ultimately did its own thing and was all the better for it. Reach completely ignored the books and was all the better for it. That's 3 different approaches that all worked for different reasons, so it's possible for a Halo game to either draw from, ignore, or draw from and ignore parts from, the books and have a successful story. 343i just needs to be more thoughtful of what they gain from taking or ignoring.