It goes beyond that, the more "renegade" Taiwan is in its rhetoric and the more the US increases the MIC investments in Taiwan the more militant China is about "repatriating" Taiwan and the faster they want it achieved.
Nobody really cares that much about renegade provinces until they seem like a threat. The US famously called Taiwan the unsinkable aircraft carrier in the pacific[1]. It doesn't really matter that Taiwanese people themselves don't want to fight China.
If the Europeans and the US were serious about Taiwan's independence they would have built up Taiwan's defense industry and supported it's independence in the UN, when they were at the height of their power, but they specifically did not, they actually voted against any attempt of Taiwan to be admitted to the UN(to be fair the Republic of China in its constitution still considers itself the sole China). At the time Taiwan was an economic powerhouse and they had some of the biggest shipyards in the world.
Right now the US cannot at all compare with China in terms of military industrial output, here's what the US Navy secretary general had to say about the topic[2]. Basically AUKUS is subsidizing US shipbuilding.
[1] https://en.wikipedia.org/wiki/Unsinkable_aircraft_carrier
[2] https://edition.cnn.com/2023/02/22/asia/us-navy-chief-china-...