To player character:
"I don't have time to explain why I don't have time to explain"

Garbled radio chatter
Turns head away:
"I will! I will!"

Could this piece of dialogue be more aimed at the player holding the controller rather than the player character? Yes, it fits in with the context of the scene, the Stanger disappearing in a rush.

There seems to be a general consensus (am I right about this?) that something didn't go quite as planned with the story in relation to Destiny's development. No one know's the circumstances or the details but the relative polish of the gameplay mechanics vs the story don't quite jive.

Could this seemingly odd line be self referential to their situation leading up to launch, and the "I will! I will" be an emphatic promise to deliver on explanation of the story and everyone's motivations over time?

I think that's a bit of a stretch, but many times the story deliberately raises questions to be resolved later. This is definitely one of those times.

I feel like this is Destiny's whole story summed up...

There seems to be a general consensus (am I right about this?) that something didn't go quite as planned with the story in relation to Destiny's development. No one know's the circumstances or the details but the relative polish of the gameplay mechanics vs the story don't quite jive.

I think there's a general consensus that with regards to storytelling, Destiny is almost certainly quite different, and in the minds of many, not quite as good as the best parts of the Halo series (although which ones you think are best differ).

I think there's a general consensus on Reddit that Bungie are lying jerks who stole our bibles and shot our dogs.

I'll probably write at length about this at some point, but I do believe that the differing aims of Destiny's design put it at odds with the traditional model established by Halo, with a feature-length, linear story presented in cutscenes punctuated by long action sequences directed by the player who controls the story's protagonist. At some times, Destiny seems to want to ape this, and at others, it seems to want to distance itself from this. Whether this is because the game's nature is at conflict with itself, or because there were conflicting viewpoints amongst its developers, I don't think I can really guess.

Reddit seems to think that Joe Staten's departure very late in the game's development cycle somehow caused a huge disruption, not just to writing but to lots of other areas, and that just doesn't make sense to me.

I think we're going to get a story that's broader but less deep, and spread out more between sequels and DLC, with less focus (but not eliminated focus) on a single heroic protagonist.