Here is where I kind of stop agreeing. Master Chief's biggest strength is adapting, it isn't new for him at all. He is very comfortable with it.
In the books he works solo, or at least is more than willing to, all the time. In Halo 3 he did quite well without her.
He is quite good at taking orders from superiors as we have seen him do throughout the game: he is a weapon at the disposals of those superiors. Having him do all that on his own won't really be a stretch for him.

One situation that we haven't seen him in though (in the games), is going it alone deep in Covenant/Forerunning territory. Interfacing with alien technology has been Cortana's most important ability and has been the biggest help to the Chief so far. Without that, it will be a serious challenge for him to navigate.
This opens up a great new possibility as well, brought up by Apollo, of Chief's Geas unlocked by the Librarian acting as a "new" Cortana. Insofar as helping the Chief interface with Forerunner tech anyway. That does sound like an interesting way for the series to go.

(I still want to see Cortana back as a villain though. hehe)

I do agree though, that doing it while recovering from the loss of a loved one
: Now that she is gone, one of his closest links to humanity, how will he
: deal with this all? There are so many factors at play, hinted at, and
: hidden from us, that the Master Chief will not be someplace comfortable
: once Halo 5 rolls in.

: It could force his character to evolve, to change, and to perhaps, regain his
: humanity as 343i vidocs have all hinted at. They stated Halo 4 would be
: the first act in John's personal story, so with everything going on and no
: longer having Cortana with him, he would have to act a lot more
: independently rather than needing someone else.

: The Master Chief is a proven hero, I agree, but it relies on other things
: beside combat. Most of the times, he usually followed either Cortana or
: his superior's orders, and I'm of the belief that a person never really
: stops learning. He may have yet some road still ahead of him.