What is the US counter to this Chinese counter? Did I suggest something you hadn't considered, or am I missing a nuance of this strategy?
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Yes, you are missing a lot of things, and they aren't even 'nuance.' It is becoming increasingly clear to me that the reason you have the perspective and opinion that you do, is because you have no idea how naval and carrier warfare work at all.
First off, if China gets into a shooting war with the US, it's lost. This is the literal worst possible outcome for them, so they're very unlikely to start one.
Second off, Chinese Destroyers, Subs, etc, are going to be
nowhere near a US Carrier in the event that China is mobilizing towards war. At a minimum the large escorting fleet will be keeping them out of visual range of the Carrier, more likely they won't be within 50-100 nautical miles. If they're anywhere remotely close when China starts shooting at Taiwan, they will be ordered to leave the area, as China is clearly in a war-starting mood. If they refuse, boarding parties will be sent to enforce the order. If they shoot at the boarding parties, then again, China has started a shooting war with the USA.
Third off, as Marduk mentioned, a Carrier being within half a thousand miles is within easy striking range of an area, and thus enforcement of a naval interdict.
Fourth off, the overwhelming majority of PLAAF aircraft are complete crap. We're talking generation 3 or earlier. They have some Soviet generation 4, and some of their own knock-offs of soviet generation 4. Soviet aircraft historically perform at a 3:1 or worse loss ratio against American aircraft of equivalent generation, and if anything, the PLAAF is likely to do worse, not better. Most front-line engagements would be American Gen 5 or Gen 4.5 aircraft, giving an even larger advantage to the US side of such a conflict.
The J-20
might live somewhere close to up to its hype, which would make it a clear threat to US Gen 4.5 and non-ignorable threat to Gen 5 aircraft. Even if it does though, which is questionable as they've had problems getting fully-functional engines into those bad enough that the world at large knows about them, they have a few dozen of them, the US has
hundreds of Gen 5 and Gen 4.5 aircraft.
Fifth off, even
if China manages, despite inferior training, inferior equipment, and an utter lack of actual war-fighting experience, to sink one or both Carrier groups in the region?
They are
still completely and utterly screwed. They will have killed thousands of American sailors because the US tried to move merchant shipping out of a war zone. This is a clear,
massive Casus Belli, on the order of Pearl Harbor, and it does nothing about the other 8 active Supercarriers, probably half of which will vector directly to the area, or Okinawa, or Yokosuka, or the US sub fleet, or the rest of those carrier battle groups.
Things immediately escalate to a full-scale war. Every Chinese naval base that is not within range of mainland China's AA envelope will be crushed within days, every merchant ship flying the Chinese flag will be captured or sunk. Within a couple of weeks, when all redeployed forces are sent into the area, what's left of the PLAAF will be torn to shreds, and systematic bombing of all military infrastructure begins.
Depending on what classified programs exist, Chinese long-range nuclear capability might get knocked out pre-emptively, and if
that happens, the bombings will continue until the CCP surrenders unconditionally. This last is more of a pipe dream, but it's more likely than the PLAN being able to beat the USN, without active political sabotage by US civilian leadership.