Here is a thought experiment. If Taiwan did not exist, would the US and China still be at loggerheads? My hunch is yes. Antagonism between top dogs and rising powers is part of the human story.
The follow-up is whether such tensions would persist if China were a democracy rather than a one-party state. That is harder to say but it is not obvious that an elected Chinese government would feel any less resentful of the US-led global order. It is also hard to imagine the circumstances in which America would willingly share the limelight.