Do you expect complex character depth in a game about a plumber rescuing a princess from a spiky turtle king?
I'd say it helped Sonic, but I guess that's besides the point. Who said you need a "complex" character to have a story? Mario & Luigi Superstar Sage is the perfect example of how Mario with a story could look like. Has the charm and humor of any other Mario game, but a legitimate story that is continuous throughout a series of games.
Hell, what they're doing with Odyssey and what was done with Galaxy is a step in the right direction imo. Just needs to be connected. If there was a little more exposition, they wouldn't be too far off from the "Sonic" series you're comparing it to.
Odyssey's premise and theme reminds me a lot about Sonic Unleashed. Mario (Sonic) meets a cute new ally that may or may not be connected to the final boss, and the two travel the globe to fix the turmoil their respective villains have caused.
I literally just played a game where Sonic jumped into the Presidents limo so he could infiltrate a moon base that Eggmans father developed.
Mario should never do anything like that and it has never come close. ---