Nintendo of woe

A recent MIT prank (or "hack" as the kids call it) has got me thinking about Mario.
I mean, he's a plumber, but we have never seen Mario actually work. We've seen Mario play golf, tennis, soccer and baseball; we've seen Mario save the princess of the Mushroom Kingdom innumerable times, go up against both a giant ape and a dinosaur-looking thing (what the hell is Bowser?), and ride an actual dinosaur. And yet Mario has not engaged in plumbing activities. Is he independently wealthy, taking up plumbing as a kind of side hobby? Is Mario just so lousy a plumber that his services are not in demand at all? Or does Luigi run the family plumbing business (it would explain his frequent absenteeism, though it would call Luigi's Mansion into question)?
For that matter, why have we never seen the duo's parents? We've seen both Mario and Luigi as babies, yet they seem to be entirely without parental supervision. Not only that, but they were wearing the exact same style of clothing as babies. Were they forced into plumbing at infancy? That would explain why they seem to have such aversion to plumbing now.
Oh, Mario, you crazy plumber of mystery.