That would be a very bad and dangerous assumption. The issue/strategy here is not what each nation considers to be theirs. The strategy is to secure the borders and the area near the borders. Taiwan is less important as an entity of China than it is as a place where a foreign nation can stage forces. This is why China is doing what it is doing in the SCS. It wants to push any potential fight as far off its shows as it can.Great points save for this; Taiwan is non negotiable, China will not haggle over something that is china’s by right and by law.
Anglo america have proven they lack the stomach for a fight and that may change when they elect a Christian fundamentalist like Cotton into power but by that time, PLA force projection should also extend to the Caribbean.
There may, due to cost and technology, become a time where the US views any potential fight near China as too expensive. By that same philosophy as above, however, the US would much rather have a war in Korea, Japan and Taiwan than in the US itself.