I am not expert in these things, but let me take a crack at your question: China's objective could be to absorb Taiwan.

Neither China nor the USA are (hopefully) willing to ignite WWIII over Taiwan, still I could imagine that the ability of the USA to keep its carriers in theater could make all the difference in outcomes with Taiwan.

Imagine as this heat up the USA tries to stand firm with Taiwan and keep its military close by. China pushes back, eventually it comes to a very limited attack maybe hitting the least vessel within the carrier group, or perhaps even just drops a missle exploding in 100 yards directly in the path of the carrier. The message is clear. We can blow you up anytime we want. And if you don't leave eventually we will. So the USA withdraws and Taiwan seeing there is no cavalry capable of coming to the rescue simply surrenders to China.

By contrast imagine if the China attempts this, but he USA shoots down every hyper sonic sent its way. Well now emboldened the USA stands firm and Taiwan decides differently.

So it seems there could be an objective here that would make sense. right?