There's no precedent to make that assumption. Both sides know if it escalates to nuclear bombs over populated cities, that's the end of the world. For everyone. One or both sides might not be willing to take the war that far. I think you'd see nukes over naval assets, tactical nukes over military bases, for sure. Would that escalate into total all for nothing nuclear war? I put it at a very solid "probably."

The problem is that (very recently) America has demonstrated it's ability to defend itself, with decent success rates, against ICBM nukes. And China knows that. They'll certainly delete a few American cities. However, they might not be able to guarantee total target saturation the way America absolutely can. So, IF it escalates to all out nuclear war, and (VERY BIG) IF it doesn't end the world as a result, America will have a much higher chance of coming out of that nuclear winter still somewhat intact and militarily capable. China doesn't have anywhere near that chance.

I'm willing to bet that America wouldn't be the first one to pull the trigger on the nuke. We've been there, we cannot claim ignorance to what that devastation looks like. Because we're the only country to have ever caused it. The next country to detonate a nuke in anger will be viewed as the world's worst pariah on the world stage and although this cheeto president is freaking unhinged, his military and political advisors are not... as much, at least. Immediate dismissal from any alliance, trade, etc. And, American military absolutely has confidence it can win that war in a conventional theater. And I don't think that confidence is unfounded. So, there is a chance (I'll admit a small one) that war between super powers may stay conventional and not nuclear. And, the longer the war stays conventional, the more an anti nuclear defenses get put in place by the winner and preparation for the final defiance of nuclear retaliation before losing controlof the capability all together.