Earlier quoted context omitted.
It seems like a number of superhero comics (which I am lacking in citations for) have focused on the idea of the superhero as more a symbol rather than a person. Any worthy successor can pick up the mask/costume/cape and continue fighting crime in the name of Fooman, and thus Fooman becomes a legend rather than a single person. In the words of The Sandlot, "Heroes get remembered, but legends never die." The Dark Knig…
That scene in The Dark Knight is adapted from a storyline in Frank Miller's The Dark Knight Returns . If I recall the original, Batman's retirement makes people sufficiently nervous that a gangs of young kids dress like him and do their own crime fighting. The original Batman has to clean up after them as well.
So you got a number of the main points right.