Well the stories were always about as minimal as they come, so this one easily lived up to that standard lol

I was happy with it... the idea of having the story exist almost entirely in discoverable memories was brilliant as it really allowed you to do whatever the heck you wanted.

It wasn't a great story, but this game wasn't really about the story as far as the experience is concerned.

The story...it feels kind of empty to me. There is a story, it's a simple story but it leaves a lot to be desired, I think.

Not even halfway through the memories and only have one dungeon finished, but so far so good

Though I'm generally fine with decent stories since I've played so many JRPGs with little to no story anyways. As long as it's not obnoxious or overly stupid and repetitive, then I'm fine and this game doesn't fall into either of those categories

I didn't care about the story one bit during my playthrough, but I wasn't really disappointed or anything since I don't go into a Zelda game expecting a good story.

I watched the memories mostly in one sitting (I loved the picture puzzles), so that's probably part of why it was more memorable, but to fair, you also have the option to watch them at any point, not just when they're first unlocked.

The Zelda memories are all connected for the most part, so once you piece them all together, you'll understand the heavy burdens she's forced to deal with from both her father and her citizens, and her frustrations as she continously fails at achieving her divine powers, all the while growing closer to Link. This is amplified further by the various diaries you find, particularly the one in Zelda's bedroom. This all culminates nicely in the 13th memory, where Zelda finally releases her sealing power in an act of desperation to save Link. I just loved the way it all came together.  

Of course, the game focuses first and foremost on exploration, so the survival, traversal, and combat like you stated are also key to how memorable the game is. At the same time though, I definitely found the narrative to be well done, and while I can see why it might dissapoint people who prefer a more linear approach, I definitely loved the way the narrative was handled here. This is definitely my favorite incarnation of Zelda (and Zelink) so far.

Strictly speaking story, it's not that great, nor that much different from past Zelda games, but the game overall in comparison to the trailer, my expectations were blown away, mostly because this was the 1st time I've seen this trailer, and I am sure glad I skipped it. I feel I enjoyed the game so much more by doing so. All the moments shown in the trailer I got to see 1st hand playing, and they were so fun and exciting. I feel some of that would have been lost if I had seen this trailer prior to playing.

Thank goodness I did the Zelda blackout. I feel I enjoyed BotW so much more as a result.

No.

It's many things - the best in house Nintendo game probably ever, easily the best Zelda game and one of the best open world games ever. That story however, suffers from "open world's disease".

Metacritic says differently. 

I would have like a few more dungeons as part of the story, there is lots to do in the game but still a big short on the real story.

Loved.
The final memory is maybe the best Zelda scene.