You certainly do. A global nuclear war wouldn't even remotely come close to ending warfare. Immediately after the nukes stopped flying, traditional military conflict would follow/continue, including intense territorial landgrabs. Whatever is left of Russia, as one example, would be attempting territorial annexation of any parts of nearby Eastern Europe that hadn't been destroyed, as a desperate move to grab resources (including food). The US could hit Russia with all of its nukes and Russia would still have 100+ million people and vast military resources that dwarf its neighbors.
You could simultaneously detonate every functional nuclear weapon on earth inside of the borders of Texas and still not manage to kill everyone in the state. The notion that global nuclear war would end all of civilization, has always been a good form of propaganda aimed at preventing nations from doing something so stupid. The earth is really, really big.
I thought the problem was more the nuclear winter that would follow nuclear war? If a volcano explosion can cause a mini-ice-age, I don't see why burning every major city on earth wouldn't cause enough of an ice age to cause a civilization-killing famine. Not to mention, the poisoning of substantial amounts of water, and food sources would mean that a lot of what was left over would be carcinogenic.
You could simultaneously detonate every functional nuclear weapon on earth inside of the borders of Texas and still not manage to kill everyone in the state. The notion that global nuclear war would end all of civilization, has always been a good form of propaganda aimed at preventing nations from doing something so stupid. The earth is really, really big.