The problem is not playing the game for the story. The problem was with expectation, false marketing and knowledge that there was a story at one point.
The more I think about the story in Destiny, the more it pisses me off (unlike ME3 where I was instantly raging). It pretends to be so much with the intro cinematic, shown weeks in advance for marketing purposes by the way, big talks about the Traveler, the Darkness, saving the Last City on Earth. The game's motto is "Become Legend" the game is called "Destiny" - very pretentious words.
If the game was supposed to be loot farming and PvP, there's no becoming Legend here. Hell, Diablo 3 had at least a proper, albeit poorly written, storyline with you kicking ass and becoming, effectively a superhero.
What do we do in Destiny? Why am I the chosen one? Apprently I'm so very special that the Exo-Stranger was already observing me when I first got resurrected on Earth... was she there by coincidence?
Every mission in Destiny, every word is full of pompous crap: the "legendary" Sword of Crota, the "eternal" Vex, the "mythical" Black Garden. The Moon Strike states that a "terrible" darkness is being summoned on the Moon, and it ends up being a bigger version of the Ogre? This game is all tell but no show. You are told that you do great things, but the very gameplay is not supporting the premise. Darkness is just a bunch of warring alien races that you slaughter by thousands, Vex are just a faction, Black Garden is....
???
This game has nothing! It has no character who has any personality. Voice actors are wasted: do you seriously believe they would hire Lance Reddick, Gina Torres and Nathan Fillion (Firefly cast: bonus points) and use them for providing loading screen voiceover and a phrase or two as Tower Vendors? If so, what a disappointment.
The missions are also wasted: we go from freeing an AI, to wielding a super-sword to killing the most dangerous aliens in the galaxy and nothing is joined, nothing makes sense. The Vex who live in all times are just the Fallen with Teleport. There's no indication that any "evil" alien race is worse than the other, apart from what you're being told.
And here's the biggest point: you are Fry from Futurama, stuck 1000 years in the future working as a delivery boy. Ghost tells you to kill aliens, you kill. Ghost tells you to go to moon, you go. Exo-stranger tells you to go to Venus, you go. Speaker tells you nothing, you don't ask. Cryptarch cheats you and gives you blues while keeping legendries all for himself, you don't discharge a shotgun in his face. What a push-around!
The most basic parts of storytelling are not present in Destiny: compelling characters, palpable storyline, hero development, coherent world. We got nothing: characters have at most one cutscene, apart from Ghost, who has no personality, the storyline is non-existent and overdramatic at the same time, your character is a non-entity, the world doesn't make sense. Was it too much to ask to have at least one of these things?
And that's what we're left with: a shell of a game where your protagonist is only defined by his or her clothes and endless grind. A shell of what it could be and a disappointment for sure. What a waste...