To understand the strategic importance of Taiwan, just look at a map. It lies in the middle of the principal sea lane to Japan and South Korea. If America ultimately chooses to acquiesce to a PRC takeover of the island, the Chinese will have a foot on the necks of those two countries.
Then what? Neither Japan nor South Korea is in any position to wage war against China. They will turn into vassal states; their current liberal democratic systems will remain in place, but they will be required to follow the Chinese line in everything that matters.
In other words, it will be a big step in the reconstruction of the Chinese Empire. Everything old is new again.