War is but a continuation of politics itself. What is the political objective in using Nukes. I would say almost none, because neither the US or China is aiming to annihilate each other.I don't know why are we ruling out nuclear war? If China wins in any measure, The USA and its goons will use it.
US is trying to roll back China's expansion into the SCS and contain Chinese influence in EU and abroad. None of these objects need to involve Nukes.
China is also not going to use nukes unless the survival of the state is in jeopardy or US troops land on China mainland in significant numbers.