Face value has little to do with it. That is what the plot of The Dark Knight is about:
Batman has reduced crime severely at the start of TDK. The criminal underworld, or what remains of it, cowers in fear. Bruce Wayne realizes Batman may no longer be needed, and he is looking for Harvey Dent to step in, so he can retire. That is when the Joker steps in and confronts the gangs of Gotham during their group therapy session with Lou, warning them that Lou is untrustworthy and not as untouchable as they think. Because as he points out, Batman has no need for jurisdiction, he can get to anyone anywhere. This turns out to be true, because Batman flies to China and delivers Lou on Gotham's doorstep. With Harvey stepping up, Bruce is ready to retire the cowl.
And then the plot of the Dark Knight Rises:
Bruce IS retired as Batman, and severely out of shape. That is literally how the movie starts. Gotham no longer needs Batman. Batman is now a wanted criminal, and Dent is a hero, all based on a lie.
Now, whether any of this is realistic is besides the point. This is a fictional city, set in a fictional universe, obeying by laws that make the superhero the good guy and not the villain. In Batman's Gotham, Batman makes a difference and reduces crime. And he does so effectively in the Nolan movies.
In real life, a person like Bruce Wayne could probably dramatically reduce poverty, and thereby reduce crime. But in his own universe, the real issue in Gotham is crime and corruption. Gotham needs Batman, and Batman eventually is able to reduce crime to the point where he is no longer needed.