I'm also not convinced that the per capita crime *rate* is that much higher in most downtowns. The raw numbers are higher yes, but there are also way more people. Unless you go to a skid row or red light district type place, but, once again, the existence of those places is a sign of the failure of capitalism and the government to protect people, NOT side effect of living close together.
Humans aren't betta fish. We're not going to start instinctively killing each other if we get too close.