As a disclaimer, these kind of "why not questions" are often a bit hard to answer, as it can be difficult to state exactly why something that could have happened didn't.

With that said, some explanations can be given. First of all, consider the position of Taiwan vis a vis China. For millennia, the position in China was that the Middle Kingdom was positioned between the four oceans, meaning that it was bordered by the Pacific Ocean to the east. This means major islands in this ocean would not be considered as part of China. In fact, pre-Qing Chinese sources were very explicit that Taiwan was the first of the foreign countries, and therefore not a part of China.

This is significant, because historically, Chinese people have only to a limited extent consducted settler colonialism in areas explicitly thought of as being outside China. Rather, China have expanded through the gradual assimilation of southern tribes. Taiwan being an island had a natural barrier against this process.

The second factor to consider is that colonization is not necessarily easy. Tonio Andrade has pointed out that European colonial enterprises only succeeded with state backing. Since the Chinese state, at least until the Ming dynasty, never regarded Taiwan as a part of China, it had no reason to back a colonization of the island. Recall that the Taiwanese aboriginals did not pose any threat to people outside the island, so if you were not interested in Taiwan itself, there was little reason to extend your rule to the island. Ordianry settlers needed the protection of a state framework to succeed, and until the 1600's they simply didn't have this.

So what changed? The first thing to recall is that the first major wave of colonization of Taiwan in the 1600'es did not happen under Chinese rule, but inf act under the Dutch period in Taiwan. The Dutch imported Chinese laborers from mainland China by offering them land and a chance ot settle down. Eventually, the Chinese population outnumbered the Dutch by 10 to 1. These Chinese colonizers moved to Taiwan to escape famine and war in China. Of course, there had been famine and war in China earlier, but this time, there was a state on Taiwan that backed them and provided them with protection from aboriginals. Only this framework was not Chinese, it was Dutch.

Ironically, this ended up putting the cart befor ehte horse, so to speak. Now that there was a large Chinese population on Taiwan, it attracted the attention of state forces on China. Hence the Dutch were evicted by Zheng Chenggong in 1662, and he established the first Chinese state on the island. He wanted to use Taiwan as a base for the reconquest of China, and justified his rule by claiming he was the leader of Chinese citizens on Taiwan. His successors were then defeated by the Qing dynasty, who decided to keep hold of Taiwan in order to stop it from falling into the hands of their enemies.

Tldr: In a very short version, Taiwan was never perceived as part of China until relatively recently. There was no reason for the Chinese state to take an interest in Taiwan, and therefore potential colonizers could not receive state backing. Chinese colonization of Taiwan started with the backing of the Dutch East India Company, which then led to Chinese states taking interest in the island.

To read more, I recommend "How Taiwan Became Chinese" by Tonio Andrade.