>What happens if the PRC annexes Taiwan without bloodshed?

Do you realistically see that happening? Why would the US allow that to happen when they are so reliant on it not?

https://en.m.wikipedia.org/wiki/Taiwan%E2%80%93United_States...

I don't think it's likely to happen, but it's certainly an option I would prepare for if I were the US government.

As to why the US would allow it to happen, the PRC could take steps that would make the defense of Taiwan politically undesirable to the US (threatening biological warfare is one example that comes to mind).