Yes, the US does need a compelling reason, uber-compelling, to engage in a great power, potentially nuclear conflict over Taiwan. The growth parts of the US economy depend on Taiwan, and both China and Taiwan can threaten that. Different ways and different goals but the threat is there.
I think Taiwan is a walk away situation for the US. We need TSMC intact too much, and our motivation to fight is less than China's, so the best move is to win favor with China by doing nothing, muttering about One China being official policy forever. We would then be under China's thumb for technology.
So Taiwan's best move to survive and the US best move to avoid China's thumb is to split the card deck in half. You offer half of TSMC to the US in return for a non-ambiguous defense treaty, possibly with a nuclear deterence. This is the same as declaring war, but with post-war outcomes somewhat more assured--some parts of TSMC will survive, the US could lose and still not be under China's thumb entirely, and that actually seems like how wars are de-escalated (if not avoided entirely). It could mean the war doesn't go nuclear.
Let's not mix TSMC and Taiwan together. TSMC as company can still make money even if they move all production out of Taiwan,they can move headquarter to the US and continue to thrive,whatever happens to Taiwan doesn't really affect TSMC. But the converse is not true
In other word, TSMC can live without Taiwan,but Taiwan can not live without TSMC. This is true even from a pure economic perspective,TSMC accounts for 22% TW GDP