As of right now, a single Ohio class SSBN carries 96 nuclear warheads(W76 or W88).
That is more than enough to destroy the economic potential of China.
An attack on one of our CVNs would provoke a nuclear response.
China would also instantly lose access to the US market and cancel the worth of any US bonds held. India would eventually become the big economic winner after China/US trade was undone. The Chinese would really, really hate for India to be blessed this way.
Risking devastating economic and physical destruction for a chance to assert control over Taiwan seems stupid to me.
But then history is replete with examples of just such stupidity.
Just like our nuclear response to North Korea, North Vietnam and Al-Qaeda. Oh, wait ever mind.