Real Life Superheroes...
An actual superhero in real life would be the combination of the Punisher and Batman. They would be a vigilante who kills criminals because the justice system has failed them personally. The police would be actively looking to catch them and even set up an FBI task force to bring them to justice.
The "Real Life Superheroes" are just people making the jobs of police officers much more difficult. If someone were truly serious about becoming a hero they wouldn't work within the confines of our judicial system; they would walk the line between street vigilante and hero. The world needs an actual crazy vigilante willing to do anything, including murder. You need to aim the motivation of Bernhard Goetz and the awesomeness of the God Damn Batman into one lone figure in the darkness.