In order to get the intellectual benefits of diversity, you first have to actually talk to a wide variety of people. Cities are good for challenging people's natural preference to stick with their own kind (a fairly universal social tendency known as "homophily"). Scott Simpson, who runs Take Root Consulting, relies on the diversity of his Washington, D.C., neighborhood to figure out how to connect with a range of audiences. On a typical day, Simpson might bring his laptop to the Ethiopian coffee shop, work his shift at a gay bar, and buy some fruit from the Salvadoran guys on the corner. When working on an AIDS awareness campaign, Simpson put a nonprofit in touch with some local Ethiopian, Nigerian, and Ghanaian activists. The nonprofit learned how the local groups used blunt language and national pride to connect with their communities, helping it to be more effective in its own messaging.
Even in the serendipitous city, your next door neighbor can be a world away and homophily will trump proximity. All the visual cues you might receive in a face-to-face interaction won't help if the cultural barrier is imposing enough. "Blunt language and national pride" can travel long distances and do benefit from advances in communication technologies.
In the near term, the "Flat World" is a making all the assets of living in the city more visible. Anyone from Pittsburgh can tell you about the isolation of certain neighborhoods, but proximity is worthless without connectivity. Density and diversity don't mean the same thing in each part of the big city. In the long term, the world will get less spiky. But that doesn't mean the world will start trending away from urbanization.