Once you start playing the nuclear war game, the entire scale that you measure survival and "fine" on changes fundamentally and drastically.
For example, in a full scale nuclear exchange the US simply writes off EVERY urban area. Whether they are directly hit or not, the chaos and disruption caused by such an event means that the cities will not get the food that they need and that the chaos inherent in the population trying to flee will make them basically death traps populated only by bodies inside of a week or two.
Oil refiners are also all tier one nuclear strike targets in a full scale exchange. Effectively instantly, the entire gasoline production base in the US will be shut down.
The entire satellite grid is likewise gone, a full scale nuclear exchange will see the PRC or Russia simply writing off their own space assets as the price of crippling US space assets and they will do high atmosphere nuclear detonations geared to producing EMP's that will fry basically everything in space.
Natural gas pipelines are also targets, for the purpose of shutting down power plants.
Critical road and rail bridges are also priority targets, for the purpose of fracturing the food distribution network to the greatest extent possible.
So the nuclear exchange ends and the US population is left facing massive, crippling, issues with the food supply network. You are likely to see at least as many dead inside of a month from secondary causes as you are to see dead in the actual nuclear strikes.
Go global and the situation is just as bad or worse. If a proper nuclear war happens, there is not major power that doesn't get fucked. For example, the US and Russia nuke one another and both of them are going to spare a few nukes for the PRC as well (and Paris and London and Tokyo etc.). Full scale nuclear war makes it a game of national survival; you cripple everyone who is in a position to come after you while you are weakened from the exchange.
Even ignoring that, you are looking at global disruptions in EVERY market. Global shortages of every critical good and service. That is global famine that will kill one to two billion, at least, on its own. That is global de-industrialization as all of the needed input infrastructure is simply no longer available. You think a single major chip fab facility survives nuclear war, as just one example.
Then you need to account for the fact that a global nuclear war doesn't happen in a vacuum. Before or concurrent with it, you are going to see full scale, destructive, cyber warfare. Basically everything internet connected is going to end up bricked.
Would humanity survive all of this? Yes.
Would some of the nation states survive in a form that is recognizable? Yes.
Would it be the most destructive event, by any and every metric, in all of human history? Yes.