3Learning From Mistakes
You can't blame Mario for having less natural talent than Bowser. He's just a tiny plumber in a magical world where both flora and fauna are deadly to the touch. Bowser, on the other hand, is made of spikes and flame in a world where those are the most unavoidable causes of death. He's also apparently the master of industrial-level technology, while Mario relies on druid-level flowers and mushrooms for weaponry.
When your enemies have giant airships, you may want slightly more power than a fox tail provides.
When you've got that much going against you, the only way to even the odds is to adapt on the fly and innovate new strategies in the face of defeat. The good guys in the Mario Bros. universe are more like a man called "Lefty" having another try at unblocking that garbage disposal. They're so bad at learning important lessons from their mistakes that they make the bad guys from G.I. Joe look like the good guys from G.I. Joe. Defending the Mushroom Kingdom should not be hard: It's a magical kingdom of unlimited fantasy where stars are cute, flowers grant magical abilities and everything with a shell is trying to kill you.
All they would have to do is station guards at every entrance and give them very simple instructions: If someone trying to enter the mushroom kingdom has a shell, he's not allowed in. Just stop him, turn him around and get ready to do it again in 30 seconds when he bounces off something else and comes back. That's not racial profiling; that's common sense. This is a land so easy to defend that even TSA agents could manage it.
For the 40,058th time, TURN AROUND, SIR!
Bowser, meanwhile, has learned every lesson the games have to give him -- and those lessons are all "Have a party, buddy!"
Bowser gets to do whatever he wants, whenever he wants, in the full knowledge that everyone will put up with it. He ruins Mario's life almost yearly, and Mario doesn't seem to care. Repeated home invasions and sexual assaults normally lead to restraining orders, not golf invitations.
When you've abducted our girlfriend 10 times, then no, you may not come Go-Karting with us. They even invite him to the things that wouldn't make sense even if he wasn't a repeat sex offender -- call us crazy, but when someone BREATHES FIRE, you don't invite him to the Winter Olympics. It's not like Mario even gets to hit him -- Bowser is constantly being bathed in fire and dropped down bottomless chasms. Drops don't kill things in Mario-land, gravity being somewhat less powerful than homeopathy in that universe, and as for the lava, we've already mentioned how he breathes fire. That's less a fiery end than a gentle magma spa (and the one time it did anything, in New SMB, it turned him into a Dry Bones Bowser, and those things are even more unkillable).