As Steve said once: "It's Easy to fight Crime when bullets bounce of your chest, it means something when all you have is a shovel". If I GM a Mystery Men (MM) game, It is going to be equally focused on Low Powered / No Powered heros and Bizarre Powers. I come from a Vampyre / Champions recent past. I don't believe that the GM should try to kill their player's characters, but they are not protected from harm either.
The game as I see it:
Champion City has its Decent, strong, ethical, and true: Captain Amazing. But some cities aren't so lucky. For such a city it must trudge through day after day with what ever help comes its way, from who ever will help: people like Poodle Boy, Slow Thinker, Pool Shark and host of other unlikely heros that try to save the day as much as they can and still make it to work in the morning.
Most of the characters are low paid in the 'normal world' and so have little to money of 'fancy toys' like bullets proof vests and Costumes that aren't made from long underwear and Halloween stuff from Good Will, let alone martial arts training.
The Police think you are fools and nuts. the Criminals think you are jokes. But they are wrong, you are the only hope for a city full of crime.