I've never really needed any sort of emotional fulfillment from Mario games other than pure joy, so I don't see how expanding his backstory could help the core games at all. I do like the direction Nintendo takes, where they give them the necessary competence to fill any role a game might require.
Let's compare Mario to another blue-collar hero with a long history of getting caught up in unique scenarios: Homer J. Simpson. Homer's been an astronaut, a snow-plow driver, a farmer, a cop, a truck driver, a vigilante superhero, and dozens more diverse occupations, but on his business card it says "Nuclear Technician". Homer becomes whatever the episode requires, because the goal of each episode is comedy. Likewise, the goal of each Mario game is great gameplay. There was a time when The Simspons writers felt they had to explain why Homer wasn't at work each week, and they eventually abandoned that because they were too restricted. If every single game had to explain why Mario wasn't running a plumbing service in Brooklyn, everything would start to feel "samey", more so then it is now.
I prefer when they don't answer or even acknowledge those questions and instead treat the scenario and/or mechanics as if they've always been there. When you start to pay attention to a series's continuity, you start to run into problems. No better example exists than comic books; the very early ones had their superheroes coming up with new inventions or powers every month to overcome their current predicament, and this would lead to them needing reboots every ten years to normalize their abilities. I believe the term is "power creep". Superman at one time had super hypnosis, and was a super-genuis scientist.
How does this relate to Mario? Well, if he didn't have a princess to save every two years eventually the stakes would keep getting higher and higher until he'd be duking it out on an alien world with the intergalactic warlord who destroyed his home planet right before Mario became the legendary Super-Saiyan. The plots of every Mario game are roughly the same, but they are still all amazing games without evolving character arcs, storylines or anything else of that literary dribble.
Not to say I don't like games with compelling storylines and emotional engagement, but you don't need a good story to be emotionally engaging. Case in point: Portal, and the Companion Cube. Nintendo even accomplished this in Yoshi's Island, where Mario was a useless wailing brat but you still felt compelled to protect him. At least, I did.
Gordon Freeman, who has no personality other than "Left-Click to swing Crowbar", is the star of one of the most cinematic and unforgettable games of all time. And Half-Life 2 is barely recognizable as a sequel to Half-Life.
Even so, a Mario "reboot" could be done without completing reinventing the character or making its stories more complex. I've said this before, but I'd love to see a new Super Mario Bros cartoon, and I think a good show to emulate would be Adventure Time. Its storytelling is very barebones, its mythology at times inconsistent, and new characters, settings, and physical forces are introduced as quickly as they are forgotten about. A thought exercise: replace Finn with Mario, Jake with Luigi, and Princess Bubblegum with Princess Peach, and tell me it doesn't have the same feel as one of the Mario games.
Even a Mario film reboot could be done without all that nonsense the Super Mario Bros. Movie bothered with; look to Pixar's Wall-E or Up! for inspiration. Wreck-It Ralph was a great movie, but it suffered from trying to explain too much and stay consistent with its own lore. Wall-E was a walking trash compactor; yet we were emotionally engaged with him despite his being unrelatable. We see Carl's entire life in the first 20 minutes of Up!, but you couldn't name anything but the broadest details of it.
I've honestly lost where I was going with this post if you hadn't noticed it by now. My point is, a backstory isn't necessary for a character like Mario. Hell, in any great story, you should only get the details that are absolutely necessary; everything else is filler.
