I don't see this as an issue.

If I was asked to rank the importance of story, it would rank above graphics.

But - that doesn't mean a game should have a story.

A game should either have an awesome story, with lots of depth and interesting aspects (ala Fire Emblem and such)

Or

Little or no focus at story. Super Mario Galaxy, Brawl, and most Nintendo games in general are a perfect example of this.

In the 2nd type of games, story is there to tell you why you do things. That, and nothing more. That's awesome. You get an adventure with full action, and you're able to just have fun.

In the 1st type, the story is the game. You play a part of a story, not as in the previous where the story is just a small part.

These are both great. What doesn't work, is games that try to be nr 1, but have a crappy dialogue, bad story, or something like that. Nintendo makes none of these, but there are plenty of them on Wii and DS, moreso than on the others I believe (relatively to total games). I'll call this the 3rd type.

Then there's games that have a good story, but that there isn't a lot of focus on.  

Almost all Nintendo games are type nr 2, because anyone should be able to pick them up. Most gamers buy a game, not a book.

The Wii/DS have a huge lack of nr 4, but I believe that Wii/DS might have more of nr 1.

And of course, no one wants nr 3 really, but that is what is most common in games.

Well there are plenty story-driven games on both the DS and Wii, but because they are both more casual-focused systems you wont find as many as on MSs or Sonys consoles...

what constitues a good story?

Sorry, I've played the highlighted games and they're fantastic, but I wouldn't call their storylines complex. Having a few branching paths doesn't give a story sophistication. That being said, I don't think games necessarily need sophisticated stories, just as movies and novels don't.

I do think that the player-driven narrative these games have is exactly what video games demand, though. The linear, passive narrative which most story-based games adopt just doesn't belong in an interactive medium. Game developers keep cramming that square peg into a round hole anyway, because linear stories are more conventional and easier to craft.

Linear stories have their place in video games and so do player driven stories.

@Zucas

Many JRPGs have emotional and character development