(No such animal as a country called Taiwan. However there is an island called Taiwan.)
China doesn't need to invade the Republic of China. They just need to blockade it, just like Britain blockaded Germany in WW1 and WW2. The island of Taiwan would be out of fuel and food within weeks.
China invading the Republic of China would be like the US invading Hawaii. Why would you blow up your own stuff? You'd only have to spend perfectly good money to replace it.
It's World War III that deters China, not a carrier group or two.
Today that position is held by China. How long do you think that the US could replace its lost materiel and men against a country that is four times larger in population and probably ten times larger in manufacturing capacity?
The WHOLE OF THE WEST (5 eyes, Europe, and Japan) is smaller than just China alone in population and in manufacturing capacity.
We in the West won't know what's hit us when WW3 comes along. It'll be a lot worse than Germany's disastrous war against the Soviets in WW2.
I'm saying that China would like to avoid WW3.
It would not be good for business, and it also might sort of end humanity via nuclear war.
Neither the U.S. or China is going to engage in a nuclear confrontation with each other and any war over Taiwan between the two nations would be conventional (though China is waging a rather successful cyber war against the U.S.).
I believe carriers are essential to deterrence against China attacking Taiwan. I could be wrong though.