I don't really think so. That sounds like very lazy writing to me.
The type of story is more important. The characters, even super powered characters, are subservient to the story in the sense that the writer is telling a story, not "telling a character". A story doesn't have to preach or make a point, and it's way better when it doesn't, but the narrative goes along on its merry (or tortured way). The characters need to keep some sort of sense of intrigue about them even if you're only telling a banal so-called "slice of life" story. In fact with those "slice of life" ( do people in Western civilisation really lead such media-dictated self obsessed pointless human zero lives? God, I hope not ) stories the intrigue is essential. The sillhouetted figure who later becomes important, the note the character gets to read but we don't (or vice versa) are what makes a familiar narrative exciting to read and look at.
So back to supermen.
If we already know that a superman type character is invincible or close to it, then what is going to draw us in is the human element. This is why Smallville had millions of viewers and hundreds of thousands of fans, and why Superman comics have tens of thousands of readers and thousands of fans. This is also why in the best superhero stories we arrive in media res. It isn't lazy writing to begin in the middle in such cases, it's because the superheroic action is more difficult to write believably, and is fundamentally irrelevant to a character study. Focusing on the character of a protagonist, or antagonist, also means that when there is a set piece involving fantasy elements of violence, or when a brief fantastic event interpolates, it is far more impactful. Turkey at Christmas, not every night of the week.
