Cos it is a realpolitik sop, and; not specifically you, but a lot of people here seem to be taking it at its word and not "well thats bullshit but theres obvious reasons for why governements say they believe it"

there were on and off artillery duels and dogfights over the strait years before Nixon came along and he and Enlai went "lets brush this under the rug to fuck with the soviets lol"
The KMT itself has very little influence in Taiwan nowadays, DPPs calling the shots now.

The PRC has no executive, legislative or judicial control over the ROC, it pursues its own domestic, military, economy and foreign policies. it is in every sense of the word independent.

"But the one china policy"- is a realpolitik sop that was made after the sino soviet split to facilitate trade.