Taiwan just elected the most pro independence president in history:
en.m.wikipedia.org
That does not contradict with the desires of people to maintain the status quo (see my other post for details on the DPP's latest stance).
What the US is doing is
helping Taiwan maintain that status quo by enabling them to defend themselves and to make a military invasion as difficult as possible, in order to deter military moves to change the status quo.
The US never officially acknowledged that Taiwan is part of the PRC (this nuance makes a big difference). You need to read the sentence that follows to understand the meaning (I added parentheses to clarify the sentence structure, and also bolded the critical part).
"The US side declared: The United States acknowledges that all Chinese on either side of the Taiwan Strait maintain (there is but one China and that Taiwan is a part of China). The United States Government
does not challenge that position. It reaffirms its interest in a peaceful settlement of the Taiwan question by the Chinese themselves."
Note also the use of "China" instead of the "PRC". Officially the stance in Taiwan is also that it is part of "China", just that it is the ROC, not the PRC.
The US have also made multiple clarifying statements about the "One China Policy", which of course the PRC ignores and instead substitute with their own "One China Principle"
en.m.wikipedia.org
Let's make one thing clear, the PRC never ruled over Taiwan ever (just like how Russia never ruled over Ukraine). Thus it has nothing to do with "territorial integrity".
And before you bring in the UN, note the resolution only put the PRC as the representative of "China" in the UN (kicking out the previous ROC reps), it says nothing about Taiwan.
en.m.wikipedia.org