I personally wonder whether the circumstances shown in The Cage were portrayed as tremendously unusual for the Enterprise or particularly formative for Pike. I mean, sure, he was in a low point. But compare the events in the pilot to many other episodes of Star Trek and we see events that are more-or-less a matter of course. I think there's a temptation to blow it out of proportion because of the singular nature of the episode.
What I'm trying to say is that Pike would probably be at least somewhat contemplative and self-critical even on a good day. I mean, if you watch the conversation between him and the doctor at the beginning of The Cage, the doctor doesn't seem to think that Pike is acting wildly out of character—he just thinks he needs a break.
My feeling is that Pike was used more as a plot-catalyzing prop in ST:XI than a full-fledged character
. I didn't see any recognizable nods to the Pike shown in The Cage.