I'd disagree about Shadow of the Colossus. Shadow of the Colossus IS a story driven game. While the story of Shadow is told in a very minimalistic fashion I feel that it is still front and center. If it wasn't for the story, Shadow of the Colossus would have been a really mediocre experience.
The key thing is this. Team Ico decided to tell a story in a unique and creative way. Mario games are not really trying to tell a story at all.
If you want to talk Disney, let's talk Mickey Mouse. When Mickey started out he was a very mischievious character, and at times a bit of a pain in the ass. As time went on, his rough edges were smoothed out. He became friendly, cheerful, and helpful to a fault. In general, corporate mascots are cheerful and bland faces that are designed to appeal to as broad of an audience as possible. Your representative is generally the least objectionable person you could find. And that's why Mario represents Nintendo.
In addition, I think story would be intrusive in a Mario game. When I'm playing a Mario game, I simply want to pop it in and play. Honestly, if I had to sit through more than five lines of dialogue, I'd get fidgety. There are other games I play for story, but that's not what I'm looking for out of Mario.
But, why exactly is it that you feel modern Mario games are so kiddy? I've been replaying Super Mario Bros 3 lately, I've played quite a bit of NSMB, and I've been playing Super Mario 3D Land regularly since its release. I just don't see what makes Super Mario Bros 3 any more or less kid-like aside from the retro visuals, which are simply a product of its times.
For Super Mario 3 versus 3D Land and NSMB, I'd mostly have to object against music, and ennemies. The ennemies in Mario 3 were fearsome, and the music was very catchy and engaging. I can't say the same about NSMB.
@story being intrusive. That's where Sal's post and SotC make so much sense. SotC is arguable since there is an intro, and between each colossus a hint, but no more. It's very non-intrusive. It could be even zero like the examples Sal gave (flower and journey). As such, a story can be told non-verbally, Sal's post described this best.
@icon bland. Okay, that is actually discussing the topic, and it makes alot of sense. But at the same time, hasn't there been a mascot or icon that was not bland, in contrast with both Mickey and Mario? I personally hate Mickey.