Pray tell - What is in for China to negotiate the limitation of her nuclear arms in all those years when:
1. China only has 1/10th the nuclear arsenal size of the US;
China is increasing its nuclear alert posture and modernizing its capabilities. There is no need to expand its arsenal if there were a treaty that encompassed and froze the expansion of the nuclear capabilities of both countries and a new ABM treaty was in force between Russia, China and the US that would not cause a strategic nuclear imbalance. As I said, everything would depend on negotiation and this was not even done when China's resolution was simply to say that "Russia and the US must reduce their nuclear capabilities and until this is done, China will not negotiate any treaty."
2. China does not have any other strategic nuclear deterrence capabilities against the US apart from the land-based ICBMs and the meager fleet of 6x SSBNs (which probably doesn't actually quite qualify as strategic nuclear platforms when they are only armed with early JL-2s), whereas the US already has an all-encompassing strategic nuclear triad capability; and
The ICBM brigades are being modernized, and a fleet of 6x SSBNs is a minimum nuclear alert posture but would ensure second strike capability. It is a smaller nuclear force, but as I said, it would all depend on what kind of resolution could be negotiated between the countries, China has not even considered opening a negotiating channel to try to limit a nuclear military escalation.
3. China's ABM capability is still far from being as comprehensive, sophisticated and far-reaching (as in near-global coverage) as the US?
It is far away. However, the American ABM is not a reliable defense system. There is no guarantee that it would work as expected, even the SM-3. They are not reliable even against the DPRK which is limited in nuclear delivery in CONUS and has not yet been attacked. There is still even minimal deterrence.
I'd say that it'd be absolutely foolish for Beijing to limit her own nuclear arsenal, delivery platforms and ABM capability developments at the behest of the US (plus at a significant expense of herself), all while the US is already holds an overwhelming superiority over China in all of those fields.
I would not think it foolish for Beijing to limit its nuclear arsenal, as its own capabilities are modernized, maintain a low-power nuclear posture, maintain its second-strike capability, and limit American ABM development and US nuclear expansion. Everyone would win. Although China would have a disadvantage of having a smaller arsenal, it would still have deterrence and would stop the nuclear escalation that would follow.
Also, what makes you think that there isn't at least some kind of strategic-level military interactions between China and the US behind the scenes?
There is none. That is why I think that part of the recent American development of disabling a nuclear response from adversary states can be put down to the fact that China is not even willing to enter into discussions about nuclear weapons.
And if we really want to go ALL the way back - Between China and the US, China definitely isn't the first one to have nuclear-tipped weapons aimed at the opposing side.
I agree with that. However, I think it would be much more beneficial for global peace if China, even with a nuclear strike capability less than the US, negotiated a deal to halt US ABM development and its own nuclear expansion in order to avoid a nuclear escalation that will only lead the world to an even more dangerous place.