You can make a lot of stories work for a lot of different kinds of characters, but there are some some combinations that don't work.
For example, you can make a story work about Nightwing struggling with guilt because he made a choice for selfish reasons that had terrible consequences. That works for a whole lot of superheroes in the DC Universe. It doesn't work for Superman. He can make bad choices, sure, but for personal benefit? It's just doesn't fit the character. You can write the story, but it's like driving a car with square tires.
What are the stories that just don't fit with some characters?