The most common complaint fielded at Destiny is its lack of story. I think it's a little unfair as the universe has a ton of potential. But yes, the delivery of the narrative in the original release is certainly lacking. We are seeing signs of that changing in The Taken King, but we won't know for sure until next week.
Why did the narrative fail though? Bungie, known for Halo, usually have this side of things figured out. Well, matching up with long held rumours that there was once a much more coherent story, it seems the narrative had a pretty big reshuffle a year before launch. As revealed in the court case between Marty O'Donnell and Bungie, a short snippet seems to confirms the story woes. It reads:
Although Destiny was planned for release in September 2013, the story was substantially revised beginning August 2013, requiring a new release date of March 2014 and edits to much of the work previously completed
If you look at the broader context, that happened just a month before head writer on the project Joe Staten, who had worked at the company 15 years prior, left.
So yeah, we may not know why the story saw such an overhaul, but this paints a project that went through a lot of changes and some that may well have caused the main writer to leave. I'd be fascinated to find out about why this restructure was implemented and the affect it had on the story, but I don't suppose we will ever know the whole tale due to NDAs.