You are correct in you assessment. The US will not give up on Taiwan. The waterways to the South as well as to the West of Taiwan are too important, militarily. By giving up said waterways, the US, so to speak will bring the ""battle"" closer to India itself.
Right now, I would imagine the US is reassessing its military budget to meet the growing threat from mainland China and they must devise of some long term strategy to contain the Chinese influence in that area.