I heard war games indicate that the US would lose at least a few carriers if they try to defend Taiwan.

That may be more than worth it if they succeed.

Taiwan is not like Ukraine. As long as TSMC has monopoly on the latest AI chips, it's at least as important as access to oil.

The fab capacity would be gone, even if the defence succeeded. The process knowledge embedded in TSMC might survive though to rebuild it quickly.

In a war game you steel man your opponents capabilities. I highly doubt China's entirely green military does that much damage.