"strong, overarching story"
and Sonic the Hedgehog in one sentence. Wow I would have never believed to see this.
But you are right the worst thing they could do would be to take the Mario setting and try to squeeze in a storyline. An italian plumber who frees a kidnapped princess from a turtle. There is simply no way to make a good story out of this setup. But thats not the point. Its a great game because you can just play and because it allows them to create all kinds of awesome settings. A story would remove some of their freedom in creating worlds.