We're not talking about six degrees of separation, we're talking about how cities are cold anonymous places where nobody bothers to get to know their neighbor. Can you have a close knit urban neighborhood? Sure, but it requires some degree of tribalism and a lack of mobility. But in modern times that's practically unheard of. It's why urban dwellers are considered so rude, because they don't bother making social investments in a city of ten million.
My overall point is that cities should collapse under stress, which they did historically, but not anymore.