The last three Super Smash Bros games don't have a story mode though but they're doing fine.
Adventure Mode was the story for the Smash Bros games. Brawl had the Subspace Emissary and Ultimate had World of Light.
Other than that, the characters in Smash Bros. don't need a story for each and every character because they're all mascot characters with their own games and stories. Smash Bros. is popular not because it's some generic fighting game, but because of the roster of famous Nintendo characters.
I can write more on Jin Kazama from Tekken or Ryo from Street Fighter than I can for Akira Yuki.
