I know that low yield nukes wouldn't actually be that useful. I mean, they need a <100m CEP to even be a significant threat to tanks, obviously they could only hope to sink a single ship. For practical purposes they would be limited to either expensive standoffs against ships operating outside the range of China's air defense complex, or a torpedo from an SSN that managed to get in close, and would be in enormous danger afterward.
I'm not trying to endorse them as a really useful munition in their own right. I'm trying to make a point about the political elements of escalation.
If China's nuclear capability is exclusively strategic, then the Americans may reason they can use their tactical nuclear arsenal to obtain leverage in the conflict. This is especially true if they were losing. The thinking would be that if the US uses nuclear weapons in a tactical capacity then that imposes an obligation on China to either escalate or capitulate. Its only escalation option is basically MAD, so then maybe, just maybe, tactical nukes could be used to force negotiations on American terms.
Obviously Chinese leaders wouldn't back down. Even if they wanted to, the popular will for nuclear retaliation would be totally overwhelming. They wouldn't have a choice, and so then goes the strikes on Guam or Honolulu. American leaders likewise could not back down, though more from elite than popular pressure, and from there trades of cities would occur that would likely escalate to mutual destruction.
So if the US is losing conventionally and turns to tactical nukes in desperation for leverage, and China lacks tactical nuclear capability of its own, then mutual annihilation would be basically unavoidable. My point here is that having a robust tactical arsenal provides a way out of this death spiral by allowing China to retaliate to nuclear use in a way that both satisfies popular anger and avoids immediate escalation to a strategic exchange. And by making it clear to the US that such brinkmanship would get it nowhere, it makes a first use scenario less likely to happen in the first place.