What you're missing is that the US's BATNA here is awful.

America relies on Taiwan for more than just advanced-node semiconductors. The island is the linchpin in the US's island chain strategy for the Pacific theater.

Abandoning Taiwan to the CPC would have a domino effect on US relations with the Philippines, Japan, South Korea, Vietnam, etc.; let China run wild in the US backyard and gain a monopoly on some critical supply chains while holding others in peril; and is effectively tantamount to ceding the Pacific to China without a fight.

The US abandoning Taiwan is simply not an option and Taiwan knows it.