The assumptions here are still fundamentally flawed even by the standards of right-wing nuclear warfare theorists (of which I've had a few discussions with in the past), because at that point it becomes a snowball effect of both "use it or lose it" on top of the fact that a US that expends its arsenal in such a fashion also becomes open to full scale nuclear strikes from Russia or anybody else who hasn't utilized their nukes yet and has a casus belli with the US. Even North Korea's 48 strategic nuclear delivery devices would be sufficient to deal critical damage to the US, and China certainly isn't sitting still on the nuclear arms front.
The “use it or lose it” can apply in situations where both sides have a credible counterforce posture. In that situation, both sides have the capability to degrade the other’s stockpile, so any defected launch incentivises immediately using one’s own stockpile.
China’s nuclear stance is strictly second strike. It does not have a ‘launch on warning’ capability at present. This works well enough for a non-peer competitor. It works for the DPRK: any war would be existential for it, and the US won’t risk losing a few cities over it. The same calculus doesn’t necessarily play out with modern China. (Which leads to @vincent’s point that China could consider a switch to launch-on-warning.)
You’re right that Russia’s nukes will play into the US’s calculations with China. How many nukes do you think the US needs to have in reserve to deter Russia? A few hundred? A thousand? The US has 1.9k sitting in reserve: how long does it take for those to be slotted into the recently-vacated silos?