I'd say that Breath of the Wild had a relatively strong story, it was just presented in a poor way. When compared to Zelda games, I would say it really is only beaten by Skyward Sword and Twilight Princess. As far as I'm concerned, the dungeons were the point that held the game back the most. It was the polar opposite of all other Zelda games, where the dungeon play is the core of the game, while the overworld is the just where you travel from point A to B, while in Breath of the Wild, the overworld was pretty much everything, and the dungeons were essentially nothing. I will never say Breath of the Wild wasn't an amazing game, but it wasn't perfect either, and it's not my personal favorite Zelda game, simply because I enjoy Zelda most for the dungeons.
And honestly, I think a better story is almost ensured in the sequel. In most instances, you can separate the Zelda games with good stories versus the ones with not as good stories simply by looking at which games you fight Ganondorf, and which you fight Ganon. Since we've got Ganondorf in this next game, things are looking up.