This doesn't necessarily explain why Taiwan didn't invade Chinan during the ~30 years after separation, but it does explain context for what Taiwan was doing. This is paraphrasing an essay I wrote a while back.

The modern history of Taiwan began in 1895, when control of the island was handed over to Japan. Japan believed that the Taiwanese people could be assimilated into their budding empire, so Taiwanese people were allowed to study at Japanese universities and were accorded similar privileges of citizens. When the KMT received control of Taiwan in 1945, the island was economically prosperous with a solid infrastructure and a well-educated populace. Prior to the arrival of the mainlanders, Taiwan was mostly made up of three demographics: a small number of Japanese elites who ran the island, a very small and suppressed aborigine population mostly living in the mountains, and the large population of native Taiwanese whose ancestors immigrated from mainland China since the Ming dynasty. As of the 1970s, about 1% of the population was aborigine, 14% were mainlanders, and 85% were native Taiwanese.

When WWII ended and Japan was defeated, control of Taiwan was handed to the KMT, as they were considered the reigning government by the US and other western powers. While both populations (KMT and native Taiwanese) were Han Chinese, the native Taiwanese population generally came from the southwest coast of China and spoke a particular dialect almost unintelligible to certain KMT members. The KMT distrusted the Taiwanese due to their cooperation with the Japanese, while the natives disdained the less advanced mainlanders. At first, many of the Taiwanese elites spoke Japanese, but they quickly learned Mandarin to show their commitment to the new government. Mainlanders also saw Taiwan as a minor frontier colony or a backwater because they envisioned the country from a different perspective. The Kuomintang also feared that the Communists might have infiltrated Taiwan, and distrusted anyone who was not an experience Nationalist supporter. So right off the bat, there were tensions between the KMT and the natives, and the KMT had to rebuild its power base.

Remember, the KMT was coming off a severe defeat that had forced their retreat to Taiwan. While the native Taiwanese people were hoping that the arrival of Han Chinese people would remove the “glass ceiling” blocking their promotions, the KMT was much more concerned with consolidating their power and helping their cronies. Furthermore, they didn’t have nearly enough manpower to constitute a military threat because most of their forces were dedicated to controlling the mainland. Under Japanese control, there had been about 80,000 bureaucrats and 13,000 police running the island, not including the actual Japanese military force. The KMT could only afford 44,000 bureaucrats and 8,000 police officers. Chiang Kai Shek was more concerned with keeping the party and the island together than trying to take back the mainland. Bear with me for a moment, while I ignore the 2/28 incident, which was a pivotal massacre that defined KMT/Taiwanese relationships for the next 30 years.

Bruce Dickerson wrote a good essay about how Chiang Kai-Shek wanted to reorganize the KMT. Chiang Kai-Shek blamed the loss of the mainland on the organizational structure of the KMT, and it needed to be changed from the bottom up. Dickerson points out how many of the flaws related to too much energy being lost to infighting, so Chiang Kai-Shek disbanded a lot of the youth groups and ground level organizations. He also prevented many of the former leaders of these groups from rising to power. What these steps led to was Chiang Kai-Shek holding a lot more individual power, ironically similar to Mao’s moves with the Great Leap Forward and the Cultural Revolution.

Ok, back to the 2/28 incident. In the middle of the KMT’s retreat to Taiwan, Taiwanese natives were growing angry at the KMT’s failures to improve conditions, general corruption, and other economic problems. On 2/28/1947, riots broke out. While Chiang Kai-Shek was reluctant to use force, as he needed all of his military might on the mainland, he eventually sent the 21st Battalion to keep order in Taiwan. The KMT soldiers opened fire almost immediately after touching down, spraying indiscriminately into crowds on the coastal wharfs. While estimates of how many died vary depending on the source, the most conservative estimates suggested 2,000-5,000 civilians died, and few hundred soldiers were killed or wounded. Taiwanese revolutionary groups have stated figures ranging from between 10,000 and 100,000; future president Lee Teng-hui suggests 30,000. At least two soldiers were executed for insubordination. In the days that followed, the KMT specifically targeted academics, elites, and other leaders of the rebellion. About a third of the casualties from the 2/28 genocide were arrested, convicted, and/or executed after the initial landing. About half of all of the casualties were academics or politicians. This is where my interpretation differs slightly from the historiography. Some historians have claimed these casualties were only a small percent of the elites. One figure suggested that if there were 8,000 total deaths, only 0.012% of the elite class died, however, this math is garbage. I think that the author didn’t understand how percents work. Mathematically, if 10,000 elites died, and calling 5% of Taiwanese society “elite,” 3% of the elite population was killed. Furthermore, even if the true number of elites killed is insignificant, the culture of fear and subsequent arrests neutralized the ability of the Taiwanese elites to resist the Kuomintang government.

For the next several decades, the KMT used martial law as an excuse to visit dissidents and either interrogate them or make them disappear. Lee Teng-hui, who would later become president of Taiwan, described his experience as, “One day in 1969 I was suddenly woken up in the middle of the night and taken away by the Taiwan Garrison Command for several consecutive nights and days of interrogation.” He had been under surveillance since joining a rebellious student group in the aftermath of the 2/28 incident. Everyone else in the group had been arrested years prior.

The really interesting thing is how the KMT continued to set up a government to control the mainland, not just Taiwan, while not making serious moves to reclaim the mainland. In a hilariously corrupt set up, the “national” government had representatives from each province—of which Taiwan was only one. This meant that nearly all of the representatives were KMT members, not natives. Meanwhile, the KMT carefully allowed local elections, using controlled factionalization to prevent any one group from becoming too powerful.

Beginning in the 1960s, the Kuomintang’s demographics began to shift as old veterans were retired and the most powerful elites were small, locally based Taiwanese businessmen and politicians. Beginning in the 1960s, many mainlander soldiers began to retire, and the KMT struggled to fill the holes in their organization from veteran families, particularly as native Taiwanese tended to avoid the military. As private industry grew, a small “new outward-looking business elite comprised primarily of owners of small and medium-sized enterprises” became the dominant economic cohort. Many of these new elite were native Taiwanese, as expected given their proportion of the population. The KMT slowly lost the power and political capital to retake the mainland, as for many of the native Taiwanese, it wasn’t really necessary.

Sources:

Dickson, Bruce J. "The Lessons of Defeat: The Reorganization of the Kuomintang on Taiwan, 1950–52." The China Quarterly 133 (1993): 56-84. Accessed November 25, 2017.

Edmonds, Richard Louis, and Steven M. Goldstein. Taiwan in the twentieth century: a retrospective view. Cambridge: Cambridge University Press, 2001.

Harrell, Stevan, and Junjie Huang. Cultural change in postwar Taiwan. Boulder: Westview Press, 1994.

Lai, Zehan, Ramon H. Myers, and Luojia Luo. A Tragic Beginning: The Taiwan Uprising of February 28, 1947. Stanford, CA: Stanford University Press, 1991.

Lee, Teng-hui. The road to democracy: Taiwans pursuit of identity. Tokyo, Japan: PHP Institute, 1999.

Rubinstein, Murray A., ed. The Other Taiwan: 1945 to the Present. Armonk, NY: M. E. Sharpe, 1994.

Schoppa, R. Keith. Revolution and Its Past: Identities and Change in Modern Chinese History, 3rd ed. Boston: Prentice Hall, 2011.