No, you write the characters in ways consistent with their premise, personality, and past. If this allows for certain stories, then great. If it *doesn't* allow for certain stories, then that means those stories are bad ideas.
And bluntly, your attitude seems to be "I want these stories to happen, a priori, so I will do whatever I can to rationalize why they would make sense". Even if it requires warping and twisting both history and theme in order to do so. Why is it such a horrible thing to admit that "Spidey vs Kingpin" just isn't that worthwhile a story, and there are so many better things to do with both characters?