The idea of reunification is less popular than it's ever been in Taiwan since Taiwan's Nation Chengchi University started polling in the late 1990s. What you don't seem to understand is that unification is most supported among the older generations in Taiwan. With time, Taiwan will only become less open to the idea of reunification as the older generations die off. Currently less than 10% support the idea, down from nearly 20% two decades ago. You've likely never met a Taiwanese if you believe the Taiwanese population is open to the idea.

The US has also never engaged with the Houthis, except to protect marine shipping. There was never an attempt to "defeat" them by the US.