Asia is the obvious target for a nuclear war and by obvious I mean just look where the actual nuclear weapons are pointed.
'Asia' is not one big bloc or target. And where are the nuclear weapons pointed? Do you know? Does anyone? The US is tight lipped, but we can assume it's targeting military and political bases in Russia and Iran and China, not just 'every big city'. The last list exposed from the US did have targets that seemed to be little villages, but there's a whole politick behind that (just producing targets to fill up lists, push for more development/budget, et al)
NATO countries have missile interceptor technologies that would pretect them from a nuclear war. Asia has a pile of American nukes pointed at it, as well as every other asian country having nukes pointed at its neighbor.
And China doesn't? China has been preparing for a nuclear war since the 60s. An entire aspect of the population boom was to ensure they would have enough dispersed, trained and indoctrinated labor and hands to shrug off a nuclear exchange. They also have nukes pointed the other way, in enough quantity and with enough delivery systems that some of them will get through. One of the biggest PRC projects is their great underground tunnel system criss-crossing most of Eastern China that'll put the vaults of Fallout to shame.
Just the same America is a century ahead on the whole space front. So the idea they wouldn't be leaders in the federation/space environment would seem unlikely.
No, it is not. America has rapidly lost its edge in regard to space since 2011, if not 2003. China has nearly everything America does at this moment, from a X-37 analogue to heavy manned lifters, a station of its own, numerous 'civilian' agencies working on reusables, they have lunar plans and murmurs of Martian plans right behind the USA. America has no lead of note at this time. The SLS is a frankenstein, it is chained to private interests for seats, and other than a unmanned test craft has nothing special of note, a test craft, again, that the Chinese also roughly have. Whatever America can do or does do, the Chinese are right behind.
Now, in regards to Star Trek, what would help hash this out, even if the result is pro-western, is for them to actually hash out A) who was fighting who in WW3, who was the Eastern Coalition? We assume the PRC, but it could be the USSR and allies, or even India or Iran with allies. Its members are never named, possibly for ambiguity. From then, they should actually look into what nuclear warfare does and target and see what would actually be lost in an exchange, and then C) hash out what Earth did to actually crawl out of the post-atomic horror.
If it's 'Oh, the Vulcans helped the US-West-NATO alliance take over and pacify the wastes with UE/NUN/whatever', fine, but that still barely excuses why the rest of the world is so silent. Nuclear wars don't work that way, we're not screeching Saganites, because we know society survived the war, but someone came out on top. And yes, the details point to the US - mostly in the middle and Northeast- surviving better off, but it does not mean 'Asia' was wiped off the map, nor should it.
WW3 only killed 600,000,000, and we're going to have to assume this includes deaths in the not!NATO and whatever ECON was. By 2050 we should have 8,500,000,000 to 9,000,000,000 people. That still leaves 7.9-8.4 billion people, and wouldn't even cut China or India by half if it was wholly their losses. Now, post-war chaos, famine, disease; that could kill billions, sure, but even that would still leave hundreds of millions in the bigger nations. Something doesn't add up.