I think they're too busy fixing MCC and adding stuff to Halo 5 to even begin work on Halo 6. 343 is obviously more focused on the multiplayer aspect of Halo to even begin to care about the story for Halo 6, but I think they know Halo 6 won't sell without a story, so they're just delaying it until they fix MCC, then they'll take Halo 5, add more guns and make up what could never be considered a plot, even in the loosest definition. Or they're taking their time on Halo 6's story. I hope they're just taking their time.
The people fixing MCC are a small 343 team completely separate from the main team working on the next game and they also have an outside company helping as well. You can read about it here
. The blog also states that they're working on the "next Halo FPS title" as they put it since they aren't allowed to say H6 yet, but I think most will assume it's H6 so your comment about them not starting the next game yet wouldn't be correct.
"Too busy adding stuff to H5." Huh, what exactly have they been adding which is taking up all their time? We haven't had anything major added for a long time. They stated multiple times that they're done adding stuff to H5 except for playlist rotations and new Forge maps made by community members. I'll also add that I don't know their inner workings, but to say they haven't even started the next game yet is ridiculous. They most likely started their next story and their vision for H6 or whatever their next game is even before H5 was released.