My understanding based on the reports out of the military-industrial complex is that the decision over whether Taiwan falls sits pretty much entirely with the decision makers in Beijing. There isn't much the US can do about it. If they can't coerce Russia in Ukraine then they definitely can't coerce Chinese decision making about the security situation off the coast of China.
It is a bit late to use Taiwan and Ukraine as justifications for the US using a military solution. It isn't winning these fights.
The decision to invade sits with the leaders in Beijing. "The enemy gets a say", as the saying goes, and whether they would be successful is not obvious. It would be arguably the most complex amphibious invasion in history, definitely rivaling Normandy. The US has a lot of tools, both software and hardware, to bring to the fight in this scenario. Perhaps the question is on acceptable cost. There's also really only two times in the year when the weather in the Straight is calm enough to support that kind of invasion, and the sheer volume of hardware and systems they would have to move makes this kind of operation almost impossible to hide, though there are limited and imperfect ways to mask the preparation.
>It isn't winning these fights.
It absolutely is, right now, in Ukraine. The US has been able to use the Ukraine war as a massive real-time R&D laboratory for our weapons systems. The result is that Russia can no longer project naval power, their strategic air force is completely neutered, and they have tipped their hand for much of their signals and EW systems. The war is stalemated ... without the direct involvement of NATO (the wisdom of direct involvement is not relevant here).
This is to say that I disagree, there is a military solution to this problem.
I dunno, my read on Ukraine is it looks like the Ukranians are feeling their way toward some sort of a collapse. They haven't been able to stabilise the frontline, there was that discussion of lowering the mobilisation age earlier this year and the Russian negotiators don't seem to be in any hurry to make concessions. No certainty in a war but those aren't rosy signals.
Regardless, say China decides to take Taiwan. They set up a blockade with drones and missiles. If there is a counter the US has for that I haven't seen it, Taiwan pretty much disappears off the economic map. There is an interesting series of wargames [0] recently where CSIS looked at what might happen over the first 20 weeks of a blockade and it isn't pretty (let alone what presumably happens if China turns out to be willing to wage war for 12 months or more). My read on the "summery of game outcomes" section is that the US generally takes higher casualties than the Chinese, which is a not a position anyone wants to be in. Then the war drags out and we find out if the US has any idea how to manufacture ... I don't know what they'd need to maintain an attrition war like that. It looks quite hard and consequently the idea of material US support is probably a bluff. They've shown no willingness to bleed on behalf of other people.
Maybe if some sort of grand coalition of Asians comes together to fight and die protecting US hegemony in the Pacific it could work out well for the US. Crazier things have happened.
Australia, The Philippines, Japan, South Korea, the UK, and possibly France would join American military intervention. Not to mention Taiwan itself. Probably get logistical support from other places like Singapore, Thailand, etc.
American sentiment would change if mass casualties were inflicted on US troops.
This war scenario is different for Americans than Vietnam, Afghanistan, Iraq, etc. There is direct threat to the American homeland if Taiwan falls. Not to mention destroying our technology infrastructure and industry.
It is a bit late to use Taiwan and Ukraine as justifications for the US using a military solution. It isn't winning these fights.