Regarding the story:
While this game probably has the least amount of story in any Zelda game I've played, this is probably the closest to a story that follows the name of the series. The story IS THE Legend of Zelda - A young princess who is stubbornly pursuing attaining the power she needs in order to fulfill her role in the prophecies, failing to do so in spite of her best efforts until the decisive battle had ended in catastrophe in order to save Link, then once that power has awakened, knowing the only way she can fulfill her role is to contain Calamity Ganon until the day Link could come-to and aid in a final confrontation.
While I agree with James that Zelda STARTS off as whiny or demanding, the whole arc of her story really reads more like a person who is struggling to come to terms with not being able to force the awakening of her powers, and not being able to contribute meaningfully to what everyone is aware of down the pipeline despite her best efforts. Imagine being told all your life you're meant to be one of the saviors of the land as foretold by prophecy and past generations, and failing to meet those standards over and over despite your best efforts. While I wouldn't argue they earned the power of the moment of her collapsing in Link's arms crying, the thought behind it is fairly clear given the history of the franchise and fleshing out of the NPC dialogue.
Yes, the story in the game is really the events leading up to what the current Hyrule universe is in-game today. I think more could have been done to link events in the memories to some of the characters within the game. Instead of having the ghosts of champions control the divine beasts while beating them, why couldn't the NPC's you work with within each race inherit the role of champion FROM those specters in preparation for the final battle? Those NPCs are who you interact with in the game, and I think those in game interactions carry more weight than the brief cutscenes you have with the deceased champions, even if some of them have interesting characterizations.
That said, I'm nit picking on an issue of an overall delightful game that I've taken a break from but will no doubt return to once I get some real world responsibilities ironed out. I haven't felt this delighted by a Zelda game since Ocarina of Time.