It's not that Japan and South Korea going nuclear erodes US control, it's just that all proliferation is inherently destabilizing. Believe it or not, the US is not "in it for the imperialism" like, say, Russia is in Africa.
Personally I think that it's pretty much unavoidable for both. The only tricky part is not tipping the North Koreans over the edge. It's not as destabilizing as proliferation in other regions would be just because there isn't a long list of other countries that might domino afterwards.
As for the Chinese trade-to-GDP ratio, it doesn't really capture how the economy is structured, particularly how far it leans into its comparative advantage. Many EU economies have higher ratios but are not imbalanced in this fashion. Italy buys French wine and France buys Italian wine. But if the world stops driving cars tomorrow, Germany (which is more like China in this respect) is going to hurt bad.
I would also caution you against thinking that there's such a thing as "spoils" anymore - certainly not post-WW2. Just look at how expensive the fields of Ukrainian rubble are turning out to be for Russia. Obviously Russia is looking at a bigger picture, or it would be regretting the war.
In today's world, denying GDP is easy, capturing it is very hard.
I didn't characterize US control as imperialist, I characterize it as hegemonic. Much of the post WW2 treatsies in region were specifically setup to enable US security presence to uphold military hegemony via forward basing and keeping basing partners denuclearized to make them dependant on US security commitments. Nuclear domino "afterwards" is also matter of time frames and geography. If JP/SKR nuclearizes, PRC will work towards south american nuclearization in US backyard when conditions enables it, including selling all the missile and launch hardware (see Saudi). That's what US has to worry about about loosening proliferation.
Export:GDP does capture sense of limits of damage. Having only 20% (PRC), vs 50% (Germany) matters. @20%, 10% of which is trade to west, PRC is simply not export dependant, it doesn't have same exposure profile, i.e. for all the talk of PRC auto excess capacity, ~10% of production went towards export, meanwhile DE is 60%+. The difference is between a mild sprain vs spine snapping.
I think post WW3, can be like post WW2, where huge consolidation of spoils under US control after every other industrial powers was crippled. Yes, capturing GDP in peacetime against incumbent is _HARD_, especially in strategic sectors with large moats (geopolitical not just technical). So hard that what ends up being easier might be to _destroy_ concentration of GDP. PRC hitting Boeing, F35 plants, mastercard / payment processors, seven sisters data centres, severing fiber optic cables... all the stuff where US has built up disproportionate control/share via various post war momentum mechanisms opens up huge global spoils for grab. It might not be PRC doing the grabbing, as PRC will be reconstituting as well, but but sometimes it's important to not just deny, but destroy, make net negative. A builder in a 100k house and a banker in a 200k house burn each others houses down, the banker loses more, while the builder has capacity to rebuild their house faster. Everyone in neighbourhood use to goto parties at bankers house, will they go to the builder's house parties after? Maybe if the builder recovers fast enough, maybe neighbours will do their own thing. Either banker likely to lose most. Which is not to suggest destroying GDP is an "easy" decision, but it is naturally "easy" escalation once the hard decision of going to war is made.
Personally I think that it's pretty much unavoidable for both. The only tricky part is not tipping the North Koreans over the edge. It's not as destabilizing as proliferation in other regions would be just because there isn't a long list of other countries that might domino afterwards.
As for the Chinese trade-to-GDP ratio, it doesn't really capture how the economy is structured, particularly how far it leans into its comparative advantage. Many EU economies have higher ratios but are not imbalanced in this fashion. Italy buys French wine and France buys Italian wine. But if the world stops driving cars tomorrow, Germany (which is more like China in this respect) is going to hurt bad.
I would also caution you against thinking that there's such a thing as "spoils" anymore - certainly not post-WW2. Just look at how expensive the fields of Ukrainian rubble are turning out to be for Russia. Obviously Russia is looking at a bigger picture, or it would be regretting the war.
In today's world, denying GDP is easy, capturing it is very hard.