So what? That doesn't change the fact that, practically, Taiwan is Chinese. The language and writing system, if nothing else, kinda give it away. Taipei's "One China" position merely acknowledges this fact, without committing to any stance that the CCP is the legitimate government of any country.
Why would they? England itself is only a minor part of the British Isles. They would however have a chance of being part of a broader Commonwealth of Nations, were it not for a troublesome Declaration they circulated in 1776. This is why claims to "independence" should not be made carelessly, and why official U.S. policy is especially careful to avoid them wrt. Taipei.
You said that Taiwan's language and writing system made them Chinese. By that reasoning, the US would be English. But thanks for clarifying that sharing a language and writing system with another country, doesn't necessarily make you part of that country.