My understanding of comic books is that the best heroes have the epic qualities that make them fantastic and interesting, but they also have very human qualities that make it possible for the reader to identify with them. It's easy to identify with farmboy Superman despite the fact that he's fucking God in tights. It's not so easy to do so with Wonder Woman, who by definition is hardly human at all... although the Circe-curse-of-transformation thing is supposed to help her feel mortal. Or something.
I would say a "hero" is just a man or woman who makes decisions in the interest of virtues and other things people consider 'good' - love, justice, honor, etc. Villains make decisions out of vice - selfishness being the most popular. "Super" heroes or villains are called such because they can affect huge changes with their decisions, but the types of decisions aren't all that different from their mundane counterparts.
In that sense, I think guys like Lincoln or Ghandi would be Super Heroes and guys like Hitler would be Super Villains, even if they don't wear tights. They aren't called such because "superheroes" refers to a genre nowadays. The word itself doesn't mean what it says.
Analyzing human-like superheroes is viable for the same reasons that people can and should analyze characters out of Shakespeare. People can learn a lot about the human condition by studying fictional characters, because those characters typically reflect the natures of real people.
I personally think a Code with Exceptions, be they one man's code or an entire nation's code, is not desirable but also a necessity. Even in things built on absolutes, like Mathematics, you have to account for edge cases. It's just a question of (1) how many edge cases you have, and (2) can you defend them logically. If you can, then it's okay to have them.
So I have no problem with a Batman or Superman that doesn't kill unless he has to. It's a human thing to do, and there's plenty of drama to be had by testing the limits of what such men are willing to do in (often contrived) circumstances. It makes me think of whether I would do the same thing or not. And I usually come out of the thought process knowing more about myself. Which is good!
Tangentially related: my favorite depiction of what a "real world" of superheroes would be like is the Rising Stars series. Good stuff.