I started writing out a timeline but I don’t know what position you’re asking from so I will say for the sake of brevity that the US kept the KMT from being run out of all of China […] which make up its other value to the US besides geographical position.
Yes, I know about its not-so-glorious past and the White Terror. Thousands of innocent civilians were killed. It was terrible. However, I must respectfully disagree with you on the “puppet state” part. I don’t think that Taiwan is a puppet state. The US sponsoring Taiwan is a thing of the past. Neither is a pathetic diplomatic position a good reason for being a puppet state.