There is no way any war today will ever end
with just nuclear warfare. I am very sure, a case of early decapitation will only prolong the conflict when there is puny politicians suing for peace after first sabre rattling. The entirety of military doctrines of nuclear powers were built around surviving the nuclear strike, and continuing fighting, and
at least some percentage of the multi-million strong force will do just that. On top of that, the designated continuity governments which will assume control in case political leadership will be taken out will be the military, and almost certainly the most reliable, and thick headed part of it picked solely for them being able to carry orders exactly as they are told.
Now, to the argument of
@Communism . China is by far the only country which can even remotely consider "taking first strike" as an option. Nor Russian, nor US first strike will diminish even a quarter of China's industrial output. It physically cannot. Even tiny villages in China have steel mills, and power stations that will dwarf most American ones.
Nor US, nor Russia simply has enough warheads. Nukes are far from ultimate weapons. All nukes ever made by mankind taken together have less metatons than a few hundred meters asteroid, or a magnitude 9 earthquake. Even with big 4 cities somehow completely takes off the map, China will have quite a bit more industrial capacity than US+NATO.
The next thing after this disastrous scenario happens will be PLA generals coming out of their bunkers in the mountains, putting little pinks like beast, and beijingwalkers on a first seaworthy bathtub, and sending them into your direction.
Moreover, with most of country's educated elites living in megacities dead, there will be completely nobody to rebuild the political leadership, let alone negotiate with you. Our generals will have no problem making the populace eat grass if needed, for as long as needed, they after all demonstrated this capacity just 40 years ago.
Will American generals be able to the same? No