Other than small scale limited wars like Ukraine/Russia, this is undoubtedly true. The initial nuclear exchange will kill a couple of billion or so people. Destruction to infrastructure, catastrophic environmental damage, and nuclear radiation will finish off human civilization as we know it.
Yes, but if you stock up enough guns, ammo, gold, and canned food, and hide out with your harem in your bomb shelter long enough, you can become the new king of the world.
It does seem likely that “warlords” will vie with one another for precious necessities. The winner stocks up while the losers are eliminated from contention much like in Squid Games. That’s assuming, of course, that the massive radiation and the likely possibility of a nuclear winter doesn’t finish us off.