Don't assume China thinks too highly of their first aircraft carrier. They'll spend that carrier to capture Taiwan.
This is a nice report on Chinese and American naval developments.
It notes that Chinese naval developments are geared toward a Taiwan scenario. That involves attacking Taiwan and deterring or slowing down American naval intervention.
If China takes Taiwan, China would alter their naval development toward blue water operations.
Obviously, we have more than a moral responsibility to help defend a small democracy against a large autocratic state. It is in our interest to keep Chinese naval developments focused on home waters.
I would like to contest the idea that China's aircraft carriers have no role in a Taiwan scenario.
It is true that with land-based aircraft and missiles, that China doesn't need a carrier to project air power to Taiwan.
But remember that attacking Taiwan is only half of China's focus on naval development. China also needs to deter or slow down American (and Japanese) intervention. That means that China needs to deal with our carrier task forces.
Land-based missiles and aircraft, minefields, and submarines should all be sent east of Taiwan to make us think twice about pushing close to Taiwan to throw our weight into the fight. That will cause us to approach a little more carefully once we do decide to intervene.
The Chinese aircraft carrier would have a role in slowing down our intervention, too. China's first carrier was for studying and training. China's true carriers will be Chinese designed vessels. Those China probably wouldn't risk. But the old Varyag? If I was in charge of the PLAN (People's Liberation Army Navy), I'd dangle that carrier and some escorts northeast of Taiwan. As I noted, its presence would give us pause. And force us to approach more cautiously.
The final contribution of that first Chinese carrier to delaying our intervention could be to tempt us into taking the time to set up and execute the perfect naval strike mission. Sure, having sovereign pieces of US territory that serve as power projection assets is useful. And the Navy trumpets that mission in budget battles. But the Navy--deep down--wants to exercise sea control and take down another navy that tries to wrest it from us. It would be the best SINKEX, ever.
The Chinese just won't care if they lose that first carrier task force if the end result is that China has control of Taiwan.
Remember, China doesn't have to defeat our Navy (and Air Force). China just needs to hold us off long enough to defeat Taiwan. That's a big difference. And the Chinese don't have such a huge attachment to their carriers as we do for ours. We may feel good to sink a carrier with carrier air strikes after so many decades have passed since the glory days of 1942-1945 in the Pacific.
But China will give us that good feeling if it buys them the time they need to conquer Taiwan. And they'll still have their home-built carriers to build a blue water navy that will be supported by air bases on Taiwan province of the People's Republic of China.
UPDATE: I never forget that the Battle of Khe Sanh was likely a diversion for the Tet Offensive. The North Vietnamese (as one source from North Vietnam I read years ago stated) figured we'd never accept that the NVA (North Vietnamese Army) would risk four divisions to withering US firepower just for a diversion. No modern Westerner would spend lives like that. But an Asian strategist would, he said.
We would never sacrifice a carrier--a symbol of our global power--as a diversion. China would. Especially an old ex-Soviet design.
By all means, sink the Chinese carrier if it is out there. But don't forget that the objective would be to defend Taiwan to keep a democracy alive and keep the PLAN bottled up close to the coast of Asia. If that means sinking Varyag with land-based air power or an attack submarines while our carriers maneuver to fight for Taiwan, so be it.