If there is to be no character development or significant continunity in the Mario games, fine.
But what gets me is when you have games like Partners in Time, in which the plot has to basically contort itself in wild and strange ways precisely to avoid the former.
So in any other RPG, traveling back in time to encounter a younger version of the protagonist would reveal all sorts of new and interesting information about his background, upbringing, etc. But not in Partners in Time! Baby Mario, Baby Peach, and Baby Luigi are just sort of... there. Sitting there like props in the Mushroom Kingdom, forever and ever and ever.
I remember in this annotated Calvin and Hobbes treasury, Bill Watterson mentioned how he regretted giving Calvin an extended family, because it became awkward for him to have uncles and aunts who couldn't refer to Calvin's parents by their first names, and keeping Calvin's parents nameless was one of Watterson's most cherished rules of the C&H universe. As the Mario series gets more epic due to new technology, and as the Mario RPG series continues to thrive, Miyamito's "no story" rules become very difficult to enforce in practice.
Imposing no plot on a game that needs one to remain coherent can be enormously counter-productive, if the intent is to keep the franchise dynamic and interesting. There's a reason why we'll never see "Space Invaders Tennis," for instance.