It seems that superheroes will often say that their main goal is not to fight for justice themselves but rather to be an example of virtue and "inspire people" so that the job of the superhero becomes unnecessary. What exactly are they trying to inspire people to do? Go out and fight crime themselves? Make citizen's arrests? Even if you can inspire people to become better than they are, that is not going to somehow magically eradicate crime and injustice, much less stop a doomsday weapon or repel alien invaders. Civilians simply don't have the power to do these things themselves.
An interesting example of this is from the Superman: The Animated Series episode, Brave New Metropolis wherein a tyrannical parallel universe version of Superman reflects on why he seized control of Metropolis saying he thought "...that if I did enough good, people would follow my example." How can Superman expect people to do anything close to what he is capable of doing?
In Batman Begins, Bruce Wayne says "a man is just flesh and blood and can be ignored or destroyed. But as a symbol… As a symbol, I can be incorruptible, everlasting." What is the symbol of Batman supposed to inspire people to do? In the narrow context of The Dark Knight Rises it does inspire people to participate in the overthrow of Bane's regime, which was good; but situations like that are few and far between. I would think superheroes would want to inspire people to do more than just participate in political violence. But what else are ordinary citizens capable of doing?
What would be the likely intentions of writers in this genre repeatedly bringing this trope back again and again over the decades? It seems quite prevalent.