>implicitly trying to use your nuclear deterrent to protect a conventional asset
That's the point and what US does already.
Flip situation around, PRC conventional and nuclear infra is deliberately entangled to deter conventional attacks, but US planning may still attempt to hit these targets anyway. There's enough think tank papers out there that presumes US will attack targets on PRC soil with the unspoken assumption that PRC will be a rational actor and not launch on warning to indomitable standoff attacks launched from US delivery vehicles indistinguishable from strategic platforms. So why wouldn't PRC launch on warning from these type of attacks (apart from alleged no first use)? Because US has overwhelming second strike capability and even if PRC can rationalize US strike as conventional, ultimately they don't know for sure and is resigned to wait for determination regardless. Maybe they'll have ABM to intercept or try to shoot a few AA or conduct ASW in the meantime in anticipation that attack was conventional, but those are the conventional actions the escalation ladder affords.
The point is precisely to calibrate costs and resign decision making to second strike anyway. Structure deterrence and nuclear doctrine weapons so launch on warning becomes unthinkable to create escalation environment that allows conventional ir/cbm use. Hence PRC no first strike policy, and nuclear build up for credible second strike, and rocket force doctrine that they _will_ use conventional ir/icbms in force on force scenarios. All developments to spell out that PRC will definitely be using these hypersonic platforms, so work that into the strategic game theory. Otherwise why have such conventional capabilities in the first place? They're not for show just like US conventional capabilities aren't.
Because conventional capabilities don't matter if they're indistinguishable from nuclear capabilities till they impact.
Or put it another way: China launching a hypersonic kill vehicle at a US carrier is pretty much indistinguishable to China launching a tactical nuke at one. Their launch and flight profiles are identical, and while fallout is an issue, the use of a battlefield nuclear weapon wouldn't actually warrant a strategic nuclear response. From a US perspective, the issue is they lost a carrier because the nuke is going off in Chinese waters in your scenario.
But the problem is that launch is a ballistic missile. The only actual defense is that launching 1 doesn't look like a strategic nuclear strike. But let's pretend for a moment you're somehow using these in air defense: you'd be launching hundreds and there's no way to know while you have eyes that they're not a strategic strike.
The PRC won't launch - or hopefully doesn't launch - in a conventional war because the counterstrike would definitely kill them. Same reason the US doesn't. You can de-escalate a conventional war, but you can't de-escalate strategic missile launches at cities.
You can quite happily today roll out onto the battlefield and start slinging artillery fired nukes and it would be a big deal but not warrant strategic nuclear response because everyone is only in danger of losing their deployed forces, not their entire industrial base, population and environment.
>Because conventional capabilities don't matter if they're indistinguishable from nuclear capabilities till they impact.
Then wait for impact and assess. That's the entire point of having flexibility of second strike, to give options other than launch on warning. It's why SSNs exists, to make space for conventional warfare. It's the posture major powers have adopted to reduce or mitigate unknowns in case of peer warfare where both sides are going to throw everything at each other. Because they'd rather wait to be sure than end the world on a maybe.
Again from PRC perspective, almost every conventional US capability are already indistinguishable from nuclear. Especially stand off / beyond visual ordnance that will be used against PRC soil in initial SEAD wave or whatever used to penetrate A2D2. At minimum they threaten the entangled PRC conventional/nuclear infra, which is direct attack on PRC nuclear forces. So do we expect US never to attack PRC mainland? We can hope not, but it's mentioned in enough wargames / policy / think tank papers that it can't be ruled out. So a proportional conventional PRC counterstrike can't be either. Even if it elevates chance of strategic retaliation.
The best that can be done is set expectations that retaliation will be proportionally conventional before moving up the escalation ladder, i.e. US Lancers hits Dalian shipyard building new PRC carriers, PRC notifies US via hotline that 10 conventional hypersonics is going to sink CVN being retrofitted at Puget Sound within 15 minutes. It's not risk free, but everything becomes risky when things go hot.
That's the point and what US does already.
Flip situation around, PRC conventional and nuclear infra is deliberately entangled to deter conventional attacks, but US planning may still attempt to hit these targets anyway. There's enough think tank papers out there that presumes US will attack targets on PRC soil with the unspoken assumption that PRC will be a rational actor and not launch on warning to indomitable standoff attacks launched from US delivery vehicles indistinguishable from strategic platforms. So why wouldn't PRC launch on warning from these type of attacks (apart from alleged no first use)? Because US has overwhelming second strike capability and even if PRC can rationalize US strike as conventional, ultimately they don't know for sure and is resigned to wait for determination regardless. Maybe they'll have ABM to intercept or try to shoot a few AA or conduct ASW in the meantime in anticipation that attack was conventional, but those are the conventional actions the escalation ladder affords.
The point is precisely to calibrate costs and resign decision making to second strike anyway. Structure deterrence and nuclear doctrine weapons so launch on warning becomes unthinkable to create escalation environment that allows conventional ir/cbm use. Hence PRC no first strike policy, and nuclear build up for credible second strike, and rocket force doctrine that they _will_ use conventional ir/icbms in force on force scenarios. All developments to spell out that PRC will definitely be using these hypersonic platforms, so work that into the strategic game theory. Otherwise why have such conventional capabilities in the first place? They're not for show just like US conventional capabilities aren't.