The US's relationship with Taiwan is much more nuanced than that. Taiwan-US relations are actually at the closest they've ever been. For example:

1. US sells $8B of fighter jets to Taiwan (https://www.aljazeera.com/news/2019/08/approves-8bn-sale-66-...)

2. US passes the TAIPEI act, which outlines the US's strategy in dissuading Taiwan's few remaining diplomatic allies from switching recognition to China. (https://www.congress.gov/bill/115th-congress/senate-bill/340...)

3. Visa free travel in the US for Taiwanese citizens (https://www.export.gov/article?id=Taiwan-Visa-Requirements)

The US might officially not recognize Taiwan as a country, but would it sell $8B of military equipment to a country it truly believed to be China?