Mario's story isn't amazing or detailed, but there's still a story being told. Odyssey and Galaxy had a lot of love put into it in terms of storytelling.
Zelda, Metroid, and Star Fox are in the same boat.
Games like Kirby, DK, and Pokemon don't need a big story because they are designed to be accessible games and have cartoonish characters.
Paper Mario also had fantastic stories game 1 to 3 to go along with its music and gameplay.
Xenoblade Chronicles was like any other modern game with its story.
Nintendo games aren't as plot-driven as other companies but say there's none or little is off the mark.
edit: Miyamoto games only? His range is limited and sometimes outdated, but he was and is capable of delivering something with mainline Mario and Pikmin