I have to agree with Chiramu here - the Final Fantasy games have always been about story first and gameplay second, and the MMORPG titles like FFXIV are no exception (including tying content access to story completion). Besides, quests are specifically meant to be your primary way of gaining EXP, this is how you are meant to level your character, what Naoki Yoshida (FFXIV's producer and director) termed 'content based EXP' - basically, you have to learn to walk before you can run so to speak. It should also go without saying also that the story quests all explain exactly why you are going into the raid - it's not just a 'oh, it's a big scary cave so lets go kill stuff in there!' situation, each raid has an actual storyline behind it.

If you find that this is impeding your enjoyment of the game, then sadly I don't think FFXIV is for you, as storyline is the primary aspect of this game, more so than any other MMORPG probably, and SE will never change this.