It's clear that you're speaking from a political perspective, but even that gets a bit grey.
Since you don't live in China, you should know that there are hundreds of different versions of China within China itself. You could live in Shanghai and never know the reality of the China that the people of Xinjiang experience. So I would say to your points that:
1) The markets all over China are very different. 2) The talent pools all over China are very different.
If YC wants to call it YC Shangjing, (because they're primarily targeting those two markets), that would be fair. But considering China just to be Shanghai and Beijing is a bit myopic, which is why I suggested Taiwan in the first place.
Disclosure: I am a Chinese-American currently living in Northwest China, which is VERY different than Shanghai, Beijing, Guangzhou, Shenzhen, Linxia, Shenyang, etc. all of which I've visited.
Taiwan is literally the Republic of China. The leadership is descended from the same people who overcame the Japanese. Pretending the Communist Party has a monopoly on the word 'China' is uninformed and unreasonable.
Off topic, a better compromise would have been Hong Kong, inside the PRC with some degree of democracy, though less than originally promised in 1997.
However, "Taiwan is literally the Republic of China." is disingenuous considering that their government is not the one that sits in the United Nations.
I am from China mainland, having friends and colleagues from Taiwan. Don't want to see wars happen between PRC and ROC.
"China" is the name of a country. For historical reasons the "Republic of China" is one of the names of a different country, but having "China" in its name doesn't make it (a part of) China.
Most people call China "China" simply because China's current territory is closest to the China that existed before the Nationalist/Communist split. It's not a political statement. Two different countries needs two different names. Taiwan is for all intents and purposes a country but it can't declare itself one now because of military threat from China.
Yes, there are Taiwanese who want Taiwan to subjugate itself and become part of China. But all the young people I have talked to, excluding blindly patriotic Chinese, see Taiwan as Taiwan and China as China-- as two separate countries with their own economies, histories, cultures, and languages.
(1) The talent pools in Taiwan and China are different
(2) The markets in Taiwan and China are very different
Right now the Chinese market is more important than the Chinese talent pool, but both are important. Basing an accelerator in Taiwan would be good for Taiwan, but it would not meaningfully engage with the Chinese market or talent pool. It's too late in the game for that.
Even if YC's ultimately goal were political and humanitarian it would still be more effective to base the accelerator in China and use the additional leverage gained from being in China to better pursue those goals.
Disclosure: I am an American currently living in Taiwan. (edits: grammar)