Let me ask you plainly:
Are you seriously arguing that today it is the policy of the US to use nuclear weapon on China in the event of an invasion of Taiwan?
I don't why you're asking me that.
I don't know how likely it is, but my point is that your dismissive attitude towards a think tank's position on US Nuclear Policy was entirely unwarranted. Think tanks have an input on policy, that's why they exist, and some of them are extremely influential. What's even more important, is that there are many people in the political-military establishment itself who think that way too.
That said, here is my assessment.
United States is unlikely to resort to nuclear weapons while it has a very powerful array of conventional options. However, in the event that United States suffers a serious, perhaps even devastating military defeat which renders it conventional options ineffective, it may very well resort to using nuclear weapons.
Human behavior is unpredictable, and I would not count on individual policy makers holding their cool no matter what. In fact, if United States loses tends of thousands of personnel, multiple ships, dozens of aircraft in a failed attempt to preserve hegemony in WESTPAC, I hypothesize that there is a very significant chance that United States may use and escalate to nuclear weapons in an attempt to even the odds. Especially because United States will likely have an escalation advantage in a nuclear exchange due to a larger arsenal and greater strategic depth.