American Trade Interest in Taiwan

I have been reading about the American trading companies in the treaty ports of Taiwan. There were also American missionaries on the island. Lets assume that American commercial interest on the island grew to become very critical to the US trade with China. Lets assume that there a growing number of American missionaries who established schools and hospitals so that many church leaders felt that being in Taiwan was a good thing. What would be the impact if some time in the late 1800's, America purchase Taiwan from the Chinese government?
 
There would have to be some very good reason for the US to purchase Taiwan as it lies far outside the Western Hemisphere and unlike Hawaii, Midway, etc. was not occupied as a result of denying it to other powers to protect the west coast. Instead of defending the west coast, it would seem more likely to involve the US into wars with foreign powers. Why the Chinese government would sell Taiwan to the US is another question. The Chinese were not ones to alienate their patrimony willingly. Perhaps ITTL the Qing never officially annexes Taiwan and thus "sells" to the US something they think they don't technically own? IOTL, the Chinese in Taiwan fought a war against Japan's occupation that required an army of 100,000 on the island to pacify. The US simply cannot do it. I have to assume that the POD works out in a way that native inhabitants are reconciled to US rule.

However, let's go with the POD. Obvious impact is that Japan will not control Taiwan from 1895-1950. Presumable the US colonial administration prepares Taiwan for eventual self-governance which will become actual independence after the US tires of having a Pacific colony. I assume once the US decides it wants to get rid of the Philippines, Taiwan goes too. Of course, there will be one to two decades of further "tutelage" until the promised independence date. The US won't try to turn the Taiwanese into Americans unlike the sinicization and japanization campaigns, although of course English will be taught and American ways of governance and business. So the native peoples will still keep their language and allowed to keep their own cultural habits. I assume the Han Chinese in Taiwan will remain the local elite as opposed to Taiwanese aborigines, so the island will still be under heavy Chinese cultural influence. The US is unlikely to invest as much into Taiwan as the Japanese did so the economy will likely be underdeveloped compared to what it was IOTL.

With Taiwan in US hands, the Japanese may seek another part of China to occupy as part of the First Sino-Japanese War. Maybe the island of Hainan, although is very close to French Indochina and the French may object. Otherwise perhaps a prominent peninsula like the Liaodong?

US controlled Taiwan may become a major base for the Chinese republican movement, as revolutionaries go there to plot and plan. Obviously the US presence there encourages interest in US political traditions, and the Han Chinese inhabitants keeps it as part of the Chinese cultural influence.

If the US possesses both Taiwan and the Philippines, then that is a big threat to cutting off Japanese access to the South China Sea and raw materials. In the early 20th century, this will be a big source of tension.

In a WWII scenario, US Taiwan will be quickly occupied like the Philippines were. It will probably also help decide a US push to retake the island as opposed to going to Iwo Jima.

Presumably after the war Taiwan becomes independent, and is totally separate from China.

If a Chinese Civil War scenario happens, there is no fallback for Chiang Kai Shek. This may alter some of his decisions in conducting the war post-WWII as he knows there is no safe base for him to fall back to.
 
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