Who cares about Mario? Zelda always have epic and well-developed stories. Mario is just about the experience of the platforming.

Zelda does have epic storyline, just that it's adapted to the gameplay, they won't do something that won't be good enought gameplay wise. And the gameplay is so good that i agree with their choice.
And they have several story driven games, Fire Emblem may be the best example of a Nintendo game that don't sacrifice story.

You know, it's strange how Zelda games came to be known for their stories. Before the transition to 3D, Zelda games were gameplay-first, just like Mario games. There's about four paragraphs of text in the first Zelda game, and half of that text is in the intro. The second Zelda game's script could fit comfortably on ten sheets of paper. Link to the Past's story is only there to drive the gameplay and is surprisingly brief. Link's Awakening uses the story only as a foil to help make the experience more whimsical.

Something critical changed about Zelda when it transitioned to 3D. I'm not sure that change was entirely good, either. Seeing as it's caused Nintendo higher-ups to declare that they cannot define Zelda, I guess that's kind of a no-brainer.

There's your biggest example.  Twilight Princess was Nintendo catering to all those people who wanted graphic, character focused storyline and cinematics over gameplay.

In hignsight, Nintendo doesn't put gameplay over storyline.  They are one of the better companies to balance gameplay with plot and cenematics.  Just look at games like Ocarina of Time, Mario Galaxy, Paper Mario, Super Smash Bros Brawl, etc.  Even the latest games they've released like New Super Mario Bros Wii and Zelda: Spirit Tracks have featured far more cenematics than some of their past games on the N64 or SNES.  But they are still balanced nicely with the gameplay and you never find yourself getting frustrated with them.