Stating that every Mario Platformer has innovated a lot is probably overstating it, but claiming that the series never innovates is a far sillier thing to say. It's easy to forget the brilliant things that happened with each Mario platformer, because we have all of that now. Super Mario Bros, Super Mario Bros. 3 and Super Mario World all mixed up the style of the game, and influenced all platformers to come.
Then, Super Mario 64 did the same to 3D platformers as Super Mario Bros. did to the 2D platformers. Nearly all 3D platformers are made in its image.
Those 4 games are, arguably, 4 of the most important platformers in the history of platformers, because they innovated, and the innovation ended up being successful. The key with those games was that they innovated in an incredibly successful way, so that the innovation ended up being the base for nearly all future games in the genre.
The later Mario games (Sunshine, Galaxy, Galaxy 2, New Super Mario Bros, New Super Mario Bros Wii) haven't had the same level of successful innovation. Sunshine and Galaxy definitely tried out some fun stuff, but little of it is going to stick or change the 3D platformer world.
But that's little reason to state that the Super Mario franchise as a whole hasn't innovated things, because it definitely has.
