The bigger issue for US is that tied their national fate to a warlord with very dubious ability to say the least, one that's located almost right inside China.
I think later generations will see US claims over Taiwan as exceedingly stupid geopolitics.
In effect, what they're doing is like unzipping their trousers, putting their balls in their enemy's hands and then saying "come fight me".
So while because US has invested such extreme political capital in this, China may not instantly get a satisfying mass slaying out of American provocateurs, but now, if America does literally anything except successfully invade Taiwan and either annex or put it under puppet rule, America will have lost the cold war.
That's just terrible odds for them.