Maybe the reason Gotham is so riddled with crime is because all other cities have protectors with super powers(superman, flash, etc), making criminals feel safer in a city guarded by an "ordinary" human.

If I am an ordinary criminal, I would rather take my chances at Gotham City since Batman is more or less just a man and he can't be everywhere at once. On the other hand, criminals with superpower would feel fine staying at their home cities because they have the means to fight against the superhero.