I personally thought Halo 4 wasn't particularly "true" to what came before in the Bungie games. That all breaks down to subjective opinion, of course, but it felt to me like Chief and Cortana as characters both started behaving in ways that didn't make sense given their portrayals in CE-H3. Their relationship also seemed, rather suddenly, quite different from what I had taken it to be in the Bungie games. It went from being an intimate working relationship to an intimate relationship with a lot more attendant tenderness than seemed appropriate for their prior dynamic (by my interpretation) of "cop partners".
I see more direct ties to the issue present in the past handful of Star Wars movies, myself. Ignoring a legacy that people reasonably expect to hold some bearing on the future of the series creates these sorts of problems.
Personally, I think the impending death of Cortana impacted their relationship a lot. Chief was about to lose his closest ally of many years who he had strict orders to protect, which caused him to open up more. Cortana's rampancy would explain her change from buddy to subtly romantic. I didn't pick up any romantic signals from Chief, just Cortana. Like you said, this really is up for interpretation though.
Not sure I understand your Star Wars analogy. The problem with the Star Wars movies is that they essentially rebooted the universe while still maintaining that it was the same universe, causing major questions since a reboot doesn't make sense in that universe (how did the First Order grow to be the size of the Empire? Wouldn't anyone have done anything to stop it? That sort of thing). Halo 4 I think actually respected the legacy of 1-3 quite well. 3 could have easily ended the franchise were it not for the cryosleep and the Requiem tease with the Legendary ending, so 4 didn't have much to work with. 4 dealt with Requiem, as well as the ex-Covenant, and didn't need to worry about the Flood since they were supposedly completely defeated at the end of 3. Had 4 had Chief wake up to another Covenant war while the Flood was spreading throughout the galaxy again, then it would have a Star Wars problem (and that could be what Infinite's problem is depending on how they handle it).
343 has mentioned many times that this is still a sequel to 5 so they're not completely ignoring 5 at least. So I see them pulling a CE here. Start in the middle of a war, fight on a Halo, etc. Except now we've already had our Reach explaining the backstory (5) instead of having to wait for it. Really the only thing they'll potentially be abandoning then is the cliffhangers of 5 and Halo Wars 2 which I think is an acceptable trade given the situation. However, the potential for a reboot like Force Awakens where they drop Cortana and return to a Covenant War is still there and I think we can both agree we don't want that happening.