Even if most people weren't dead by then, the system would be so jammed up even text messages would be delayed by hours, if not days. I've seen what happens when an exercise involving heavy comms gets too frenetic, and the whole comms grid just locks up after a while. Then you have hazmat crews standing around in their level A gear unable to deploy, FF units pulled off to the side of the road waiting for a clear channel, and dispatchers with their heads in their hands on the console sobbing.