I'm not actually in favor of adding a plot to the Mario platformers. I'm just saying that Zelda is a series with very stern game mechanics that have been firmly set in stone (collect McGuffins to get the better sword to kill the bad guy), while Mario is a series with very stern principles that have been firmly set in stone (go through levels and jump on things until you reach the bad guy). They're not THAT different. So saying doing something for one of them is fine, but for the other it will never ever work is kind of silly.
Actually, King Antasma is mentioning a pretty fine example up there: Super Mario Galaxy. Not only does that game have probably the most well-defined Mario character ever, it also has the Toad Brigade, which are actually surprisingly coherent characters for Mario standards. Nowhere in that game do these story elements (yes, developed characters are story elements) bog down the game experience. And it just so happens that Super Mario Galaxy is one of the most critically acclaimed Mario titles of all time.
So your notion that all story elements, no matter how skillfully and with how much care to preserve the game's pacing they are implemented, will inherently "*bleep* with the game"... I call bull*bleep* on it.
That said, I've accepted the Mario Platformers' refusal to do anything new anymore. I don't care if they add whatever to the games. This point I raise just for the principle of the matter.
But to get into something I wanted to mention before all of this popped up: I just thought maybe having a different villain for a platformer might not actually be such a bad idea after all.
...but only under the condition that Bowser is playable (Mario is still the default character though, so the players don't get scared by too much new content). Imagine the novelty of being able to play as Bowser in a main series platformer. If advertised decently, it might evoke enough of a WTF factor that it would probably sell really well.