I disagree. And I have multiple reasons for this.
1. The ratio of warheads is off. There are around 350 ICBM silos in China. According to RAND, spending 2 warheads on 1 silo/hardened target means that there is a 10% chance that the silo will survive. () And current American nuclear doctrine does not call for targeting TELs that have been deployed. Thus, in a surprise first strike, China can realistically expect ~50 ICBMs to survive. And it is very likely that some IRBMs and SRBMs will survive as well, given the large stockpile of them in China. Meanwhile, strikes against other Chinese targets (like command centers) will cost the US even more warheads. Finally, keep in mind that the US has to maintain an effective nuclear deterrent against other adversaries (such as Russia). Thus, it is highly unlikely that the US will want to be placed in a position where they are so low on nukes.
2. Major population centers are likely hit as well. Think about Beijing. If there is a first strike against the Chinese nuclear C&C infrastructure, why would Beijing be spared? The Chinese leadership is there after all, and the civilians are only collateral damage. Same goes for Shanghai, which is close to a major air base and shipyard. A nuclear attack on these "military" targets will likely result in tens of millions of casualties anyways. Heck, even the US is suffering from the same issue. Case in point, San Diego is an important naval base.
3. Conditional madness does exist. Humans are not purely rational creatures. What if you are sitting in the White House and your staff members told you that your family has been nuked? What if your historical sites are destroyed in an attack? Sure, they may not look important in the grand scheme of things, but a leader that is acting irrationally in this case may choose to retaliate disproportionally due to reasons other than pure logic.
4. Imperfect information. Imagine for the moment that you have launched a first strike against China. Your generals report that everything went according to plan. But how do you know if the silos you hit are real? What if there are rail and road mobile launchers that have survived? What if China's submarines are not destroyed because they are hiding in caves? The number of nukes that China has left is a known unknown. Now you got news that NY and LA have been nuked. Do you retaliate based on the idea that China's nuclear arsenal has been depleted? What if you are wrong and China actually has 15 ICBMs? Wouldn't that mean your retaliation has caused more American cities to be nuked?