This was maybe true in 1996, but less so today (at least from what I've heard).
China is rapidly approaching naval parity with the US, and they have enough land-based anti-ship missiles to deny most surface vessels access to the Taiwan straight.
That's not even considering the logistical aspects of it all. Taiwan is 150km from the coast of China and 10,000km away from the coast of the US...
That's one of the great innovations of the US military model. Ensuring air domination allows them to effectively expand control by simply placing bases. Britain had done that in the past with naval forces but their logistic challenges are more complicated when it comes to defending supply lines.
What if they Putined their way into Taiwan? "We are going to invade, if you stop us it's nuke time". Would the US risk a nuke on their head for Taiwan?
This is wildly incorrect. The US actually had a defense agreement with Taiwan at one point, but dropped the defense provision in the 70's for rapprochement with China. However, Taiwan has been a US ally since WW2, and has at times stationed many troops there. This is not even close to true about Ukraine.
Not to mention a Chinese invasion of Taiwan would be almost trivially easy for the US to stop. It's an island, and the US has naval and air supremacy.