: Should the Master Chief's story end? That's a much different and much more
: specific question that brings me closer to a "yes" answer. But
: even then I like the idea of a Chief on the run, at odds with the UNSC,
: and searching for Cortana.

Yeah MC's arc is a harder one to answer.
I think the nature of Master Chief in relation to the Halo universe should be on par with any good superhero - in a sense, a character that is never fully "done" in their universe. Like the end of Halo 3, his quest is complete, now go into sleep mode until the next adventure (of course H3 also hinted that there was one to come). That allows the character time to sit and not get overworked or stale with too much happening over various media. Give him a significant story once in a while, but finish each, while enriching the universe with other characters and events - and not just as side, supplementary characters, but significant story arcs, characters we continue to grow and love, in addition to our 'first love' John 117. I think of, say, Jack Ryan, Batman, 007... characters that simply do not die, and always have a place for more. ymmv. :P
(though, 007's universe is centered on 007; Batman's been reinvented a few times; and Jack's sort of like 007. Perhaps Star Wars would be a better universe comparison; the stars of the movies have their arc, while the universe thrives with other stories and chars)

Anyway Master Chief should never be 100% done. It feels like that would betray his character, his role, his legacy, and his place in the franchise. (at least until he dies of old age :P then again, if Bart Simpson is still... how old...?)
Heck I could even see Cortana's arc coming to an end, and Chief's narrative working towards a new AI.

Chief & Cortana is a core story arc, but Cortana from the beginning has had a deadline. Either she must meet her fate and come to the end of her existence (in some epic way), or narratively there needs to be a feasible, believable way to have her improve past her native/technological limitation. Both can serve as good story themes. But John really is the ultimate central character of Halo.
And Spartans never die. :)