First off disputed borders are a very common occurrence in geo politics. It rarely prevents country C from recognizing both country A and country B. Outside of the Taiwan case I can't think of a situation where a border claim dispute effectively locked a country out of nearly all international forums (or crippled it to the point of having no significant voice). The situation is very unique to say the least, but let's be frank it is dysfunctional.
Secondly reunification by any method along any short or long time frame has only a small amount of public support in Taiwan. (Recent polling: https://jamestown.org/program/taiwanese-public-opinion-on-ch...). It has been on a downward trend for quite awhile. Anyone suggesting Taiwan is going to make a forceful play to establish Taiwanese control over mainland china is beyond delusional. Very sadly the likelihood of the inverse happening grows higher day by day (both in CCP leaders talking points and military displays).
Tldr I chose the words Republic of Taiwan very deliberately. :).
The trouble seems to be that Taiwan is a government in exile, having lost to the CCP. Recognizing a government in exile is very different from recognizing the independence of state. If they do maintain claims to the rest of Chinese territory they would have to renounce those before being recognized.
The PRC also claims the entirety of China, including the island of Taiwan. It’s not at all surprising that two sides of a civil war would claim the same territory. The one thing both the PRC and the KMT agree on is the definition of China.
The idea of Taiwan as separate from China is fairly recent and not widespread within Taiwan, at least so far.
> The one thing both the PRC and the KMT agree on is the definition of China
Nit: Republic of China (Taiwan) actually claims more territory than PRC, including the whole country of Mongolia, and some other territories gifted away to the Soviet Union, among others
