Your reading comprehension needs some work. I said, and I quote, "militarily crush the US in Asia". That qualifier is very important. Let me explain why that is and why your non-sequitur about what the US can do with nuclear weapons (which, incidentally, China can reciprocate) is irrelevant.
A country's hard power is a product of two factors: its resolve and its physical capability. The US has a surfeit of physical capability - although it is important to note that China is rapidly closing the gap - but severe structural deficits in resolve. Why? First, being a democracy, it has no love for protracted conflicts. Sure, knocking over the occasional tinpot dictator and coming home in time for Christmas is fun (though the US can't even do that right); but a protracted conflict against a very heavily armed and very dangerous nation-state isn't.
Second - and this is more important - since it is economically self-sufficient and geographically isolated, its survival is assured; hence, there's no existential reason for it to engage in serious warfare against a strong adversary. This is also why it will never use nuclear weapons against China: states only use nuclear weapons when there is no risk of retaliation or when their survival is threatened. China can inflict horrific retaliation and it cannot threaten America's survival without resorting to its own nuclear weapons, which it won't do because it's in the same MAD bind.
America is not going to use its nuclear weapons to prevent its prestige from being dinged for losing primacy in Asia. Make no mistake, that's all the US has on the line here: prestige and ego. It's doubtful it would even put up a fight with conventional weapons alone. China has much more on the line: survival and the righting of grievous historical wrongs. China's resolve suffers no lack, and everybody knows it.
America's allies know all of this. Their strategic planners are perfectly capable of going through the arguments I've outlined. That's why the US has to constantly signal that it stands by them, and why the American foreign policy establishment is apoplectic at Trump's banal and minor objections to the US alliance system. America is always trying to convince its allies that its resolve is greater than it actually is.
Is USA self-sufficient ? Not completely
American power is built upon the network of allies - Latin America, Middle East, Europe and Asia. Countries have tested American resolve in the past with disastrous consequences.
You are assuming an military showdown with China will be protracted. As they say assumption is mother of all fuckups.
China has no survival issues. No one is threatening the existence of China.
If China thinks she can bully her powerful neighbors she is mistaken. Everyone has noted that china has renounced her claims over Siberia. We know how many hydrogen bombs the owner of Siberia has. you are assuming south korea, japan and taiwan cannot build nuclear arsenal to deter china. Add Indonesia and Vietnam to the watch list. if your clown Kim can make nukes they can make weapons several orders of magnitude more powerful.