I agree with everything you wrote, except for nuke first strike, the u.s has no ability to first strike to eliminate all of China nuclear forces both in the past or present, simply due to the fact that China has ICBMs hidden in the 5000km long underground great wall, this will guarantee PLA second strike ability, i don't think the u.s can survive losing 10 major population centers, therefore MAD already guaranteed decades ago, let alone now
Does the americans know 100% sure how many ICBMs are in those tunnels? Highly unlikely
Let's not be ignorant. The US has a nuclear war plan for China today. It is a first-strike-only plan involving primarily Trident submarines and bombers. The US has no real second-strike plan for China, because it knows that China has no nukes close enough to the US to threaten a first strike. All of the Cold War era declassified documents of various US nuclear war plans on China are first-strike only plans. Why is the US so enthusiastically reviving the idea of forward deploying nuclear weapons so close to China's shores? So that the US can regain the capability to hit Chinese cities within as short a flight time as possible. The US defense circles have floated many times the idea of a decapitation strike on China (and also Russia) in the hopium that that would halt or stall their 2nd strike response. Russia replied to this insane idea by saying that their Perimeter system is still intact for such eventuality. China had not yet declared any counter plan for this. That doesn't mean that China doesn't have it, but the US takes this silence as a sign of weakness.US itself already knows first strike is impossible. But they're still going to threaten invasion because China is an existential threat to them.
Some random US general saying "aim for the head" to his troops, interpretating that as calling for nuclear suicide pact is as stupid as when US interpretate Chinese officials using expressions to literally mean they will crush the bones of their enemies. Its just... Lol.
The "problem" is that both China and US has something to gain despite they both being MAD capable nuclear powers, so there is hopium on both sides that nukes won't be launched.
US believes it can take Taiwan province. It has begun the irreversible process of claiming the country, similar to when Russia began claiming oblasts in the Donbass.
China meanwhile believes that if an US invasion is repelled, American non core territory and US Co-aggressors in Asia will be up for grabs.
US will become irrelevant and eventually economically ground down by China's bloc if they don't win and capture Chinese territory in an attempt to reverse the current trend of history.
On the flip side, China is blessed with economy, industry and resources, but it is not blessed in terms of having an empire. A blatant US invasion is the perfect justification for China to acquire the final pieces to become undisputed world leader.
Hence China has the no first use decision so they can smash incoming invaders with precision and hypersonic missiles guilt free. And US is very unlikely to use nukes either, in a war where they are the attackers, using nukes and incurring MAD would be extremely politically untenable.
Think about how Putin doesn't use nukes even despite Ukraine being non nuclear.
Now think of the backlash if Americans realize that Biden intends to kill them all tomorrow because of a war America themselves started over some stupid Chinese oblast 10000kms away. You'd see military mutiny and mass lynching.
There is something even worse. American defense circles today are bringing up the idea that they could somehow use low-yield nuclear weapons on China with impunity. They theorized that China could not reply US low-yield nuke strikes because China does not have equivalent tactical nukes, and that China won't use their strategic weapons in fear of a full-scale American strategic nuclear retaliation. Because America has a much larger strategic nuclear arsenal than China. This is the insane stuff being discussed in the US right now by people in the government, and the general public. And those low-yield nukes are real. There are W76-2 low yield warheads mounted in Trident missiles, and B-61 Mod 12 bombs (on low setting) in full production. Those brand new low-yield nukes have lowered the general threshold for America to use nukes. This is just not good for humanity.
My main issue is that, America is currently not taking the Chinese nuclear threat serious enough. There are still debates as to whether current Chinese nuclear stockpiles can deliver true MAD to America. This is not a good limbo to be in for China. The current declared stockpiles is not having the same deterrence effect that it had decades ago. Because right now, there are idiot Americans thinking that exchanging Los Angeles for Shanghai, to burn China down is somehow 'worth it'. You'll be surprised at how idiotic and gullible Americans think about nuclear war with China. The American elites just don't care. They have allowed more than 1 million of its citizens to die of Covid without batting an eye. They won't care about losing millions more to nuclear fire, as long as it's an 'acceptable' price for them. In the sick minds of the American jingoists, that in a general nuclear exchange, China will burn more than the US in the end. I am aware that China is not sitting on its laurels, but it is about time that they could come up with some serious statement to say that China can do MAD now, and that any nuclear attack, no matter how small will be replied with a full strategic retaliation. So don't try anything.