Fact 1: Destiny, the game, lacks story and character development which starves the player of immersion.
Fact 2: the Grimoire cards contain extensive lore that would greatly benefit the game.
Here is my suggestion, and I don't think that it's out of the question due to the fact that the cave "disturb remains" interaction was added:
When conversing with vendors and characters around the tower, by pressing R1/RB, the menu shifts and has a list of the Grimoire cards associated with that character. Shift the menu again, and you can ask that character questions/talk (which can be updated as different events occurs within Destiny).
Eg; Not everybody in the tower is going to trust Eris, so some characters may have a thing or two to say about her.
I'm not going to demand these features or anything like that, but I do believe that proper in-game interactions with these characters would immediately deliver a whole chunk of desired in-game lore and develop the vendors that we interact with on a regular basis.
Reading through the Grimoire cards, these characters have amazing stories, but not everybody realises this due to the lore's separation from the game.
Thanks for reading. :)
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As awesome as your idea is... Sadly I don't think it would be realistic for bungie to create new dialogue for all the tower characters at this point. Especially since many of the voice actors are prolific celebrities. It would cost too much and be too hard to gather them all back to record new dialogue