I agree.
There's an, I guess, famous anecdote about Sondheim wanting to make a musical out of Sunset Blvd, and Billy Wilder saying "This movie cannot be made into a musical; it can only be done as an opera." I somewhat feel the same way about Spider-Man, not in the sense that the show has to be sung-through but in that fact that the emotions behind the story are so intense.
You can't do a campy Spider-Man, though you can give him humorous lines in his fight scenes, because this is essentially the story of an alienated person whose life-defining character arc actually makes him even more alienated. And really, Mary Jane (or Gwen, depending of which storyline a scenarist chooses to go with) and Aunt May are all he's got. And that has to be played very real, because that's his grounding in his real life--what he's "really" about.