The key subtlety here is that Taiwan has not declared itself formally independent from China. The PRC in fact threatens to surely invade if Taiwan takes that formal step.
Countries supporting the broad autonomy of regions of another is more widespread than you think. A recent example were France and Germany supporting the autonomy (but not outright independence) of Luhansk and Donetsk under the Minsk agreements. The whole Bosnia affair was basically resolved by the three ethnic regions each having broad autonomy etc. I'm not sure what the army situation is like in Bosnia nowadays, but for Luhansk and Donetsk the Minsk agreements basically recognized the right of self-defence forces for these regions.
The US basically (albeit less clearly) claims that the people of Taiwan have the right to democracy and some level of self-government. It does support Taiwan in this regard, which stops short of formal recognition as an independent country... although the way Taiwan is represented abroad, ignoring the name games, is much closer to how formally independent countries are represented.
For what's worth it (since there are probably numerous such statements over the years from different US administrations, each with its own nuance); Wikipedia quotes this as indicative of the US ambiguity:
United States policy has remained ambiguous. In the House International Relations Committee on 21 April 2004, the Assistant Secretary of State for East Asian and Pacific Affairs, James A. Kelly, was asked by Rep. Grace Napolitano (D-CA) whether the United States government's commitment to Taiwan's democracy conflicted with the so-called One-China policy. He stated "In my testimony, I made the point "our One China," and I didn't really define it, and I'm not sure I very easily could define it. I can tell you what it is not. It is not the One-China policy or the One-China principle that Beijing suggests, and it may not be the definition that some would have in Taiwan. But it does convey a meaning of solidarity of a kind among the people on both sides of the straits that has been our policy for a very long time."
There is one 2007 Congressional Research Service document (also quoted therein) that states/summarizes that "U.S. policy has not recognized the PRC's sovereignty over Taiwan" but also that "U.S. policy has not recognized Taiwan as a sovereign country", essentially the conclusion being that "U.S. policy has considered Taiwan's status as unsettled".
That kind of language definitely leaves open the possibility that the US could recognize Taiwan as independent from the PRC at some point, i.e. the US position is beyond a mere call for autonomy.
It's also (perhaps) worth noting in this regard that even more ambiguous statements ... of ambiguity such as the famous UNSC resolution 1244, which
guaranteed the territorial integrity of the Federal Republic of Yugoslavia (FRY) but without explicitly committing to whether Kosovo was or wasn't part of that guarantee, while speaking of a need for a "final settlement" for the latter territory have led to Kosovo's independence being fairly broadly recognized. (Kosovo is recognized as independent by about half the UN countries, mostly Western ones, but not by China and Russia, and probably most developing countries fall in the latter category [of non-recognition] as well.) In their advisor opinion, the majority of the ICJ judges have explicitly relied on the ambiguity of UNSCR 1244 as not precluding Kosovo's independence, in conjunction with the fact that FRY had not exercised "continuing sovereignty" over Kosovo (in Kosovo's case that was due to UN temporary administration being imposed over the territory following human rights violations by FRY forces.)
So the the lack of "continuing sovereignty" of the PRC over Taiwan (as in never exercised) can indeed be argued as highly relevant, although I'm not sure if the US (through its official representatives) has elaborated on this point in re Taiwan.