I think it varies wildly depending on what you want out of your game. If we look around, there are plenty of actual examples of apocalyptic events - Hurricanes Andrew and Katrina, the earthquakes in Haiti and Japan, the nuclear accident at Chernobyl, Nagasaki, Hiroshima, the Holocaust, Cambodia under the Khmer Rouge - that don't necessarily require a world-wide event, or one that utterly disrupts society and technology, but certainly create post-apocalyptic environments in which the normal functions of society and technology are up-ended, at least locally.
I don't think losing social cohesion is what it's about. I think it's about scarcity and the need to find and keep a group of people you can trust around you.