Good analogy, except that Taiwan and the PRC are in every way shape and form separate countries. They have separate militaries, territory and political processes. We were subjects of the King, with redcoats stationed on our land.
The Taiwanese government, as constituted, can survive for decades or centuries. The PRC government is a museaum of old men and old ideas who will not survive another generation. Why would either the U.S., or Taiwan, want to fight China? All we have to do is wait them out. If we start provoking wars, that will create a real security threat that could keep hardliners of some form in power.
The presence of our Navy is enough to deter aggression on Taiwan. This is not abandoning Taiwan, it's playing smart.