The West has been supporting Taiwan for decades and is constantly worried about China taking over the island. But in practical terms... why do they care? What risks does the West face from allowing China to occupy that island?
If the world segues into another Cold War then it becomes a game of influence and alliances long term.
Credibility with allies is then crucial, else at-risk countries would quickly cut a deal if threatened.
Put it differently, had the US not fought the Korean War to a standstill and essentially rolled back North Korea's early gains, then the Cold War could have looked very different as other countries weighed their option to align with one side rather than the other.
Yet, Korea in the early 50s was very poor, much less significant than Taiwan is on the world stage nowadays.
Taiwan is a major source of semi-conductors at the latest technology cycle. Independent, that benefits the West. Subjugated, that benefits China (and puts the West in a similar situation as Europe is currently experiencing wrt Russian gas). The other producer, S Korea, being also threatened by China and liable to react if it sees Taiwan cut loose by the West.
Contrary to this question, the current status does not place an undue burden on the West, especially with the intentionally ambiguous commitments of the US. Taiwan purchases weapons for good money and could buy more if allowed to. And the West really isn't committed to doing anything to help Taiwan until the last minute.
Finally, an invaded Taiwan that turns into a Vietnam/Afghanistan style quagmire, though an unlikely scenario, could destabilize the CCP's grip on China. At the least, invading would show the world the CCP's true colors.
If one ignores any sentimental reasons why the West ought to support an established, vibrant, democracy, then one motivation for dropping support would be if we knew it would keep China as a benign, non-interventionist, power on the world stage
* (possibly involving the US/West limiting their own interventionism in return). i.e. avoid said Cold War 2? Do we know that this would indeed be the result of betraying the aspirations of the Taiwanese people not to be ruled by China?
* China being benign and nice to its people internally is irrelevant to this answer.
If like minded nations don't support each other they might eventually fall one after another. This might be a very long term consideration but probably has been proven many times in history that aggressive nations like Russia or potentially China do not get stopped easily and especially not by giving in. The idea would be that in the long term for example the freedom that US citizens enjoy is also defended in Ukraine or Taiwan at least partly. This argument can be misused to justify aggressive behavior by itself but surely a China including Taiwan that simply occupied it, is even more dangerous for the rest of the world than one without it. The alternative is some kind of constant erosion, Ukraine today, Taiwan tomorrow and so on that eventually might reach many others as well. People living in smaller nations, say Lithuania for example, probably understand that better.
To summarize: it's a together we are stronger notion. And indeed Taiwan brings a lot of capabilities in computer chips manufacturing to the table and indeed makes "the West" stronger.
In realpolitik, frustrating your opponents is a good thing, regardless of what their objectives are, as long as those objectives don't align with your own.
China is an opponent to the West. China wants to occupy Taiwan. There is no material advantage to the West if China occupies Taiwan. That's all there is to it.