It's far too simplistic to say that heroes should or shouldn't kill. James Bond, Luke Skywalker and Indiana Jones are all heroes who kill. Even if you want to limit the conversation to Superheroes you've got Wolverine, The Punisher, the old Wildstorm characters and so on.
It's all about the mieliu the hero inhabits, and their established pattern of behaviour. There are characters who shouldn't kill, or if they do it should be the final resort and a source of drama in the aftermath.
Leave Superman and Batman aside for a minute. Imagine if Kitty Pryde killed somebody, or Squirrel Girl?