> But the real problem is that Batman exists to solve a problem; Gotham has a massive crime problem, way beyond what we see in any major city in the world. And it is a city where number of crime bosses, criminal geniuses and psychopaths exist, and where they can act fairly freely.

Gotham was created for batman IMHO and not vice-versa. If someday batman dies, spiderman won't come from New York for load balancing. Why is that almost all the super-heroes have their arch-enemy in their nearby locality. They also share the same trait. For example spiderman villains are mostly mutants and nagraj villains are mostly snake which takes humanoid form.