Imagine this scenario: China postures for military action, the U.S does not intent to interfere. Rather than "abandon it's ally" the U.S puts on a show of strength, joint military exercises, recommitting to the defense of Taiwan, the whole 9 yards. Quietly however, the U.S. withdraws support for secessionist factions within Taiwan, shifting the fragile equilibrium. pro-china factions gain power quickly, the weakening direct U.S support combined with China's military posturing drives moderates and anti-war secessionists towards the pro-china faction. With the balance of power now in their favor, mainland + the pro-china factions ramp up propaganda efforts, strengthening ties, eventually setting the stage for reunification. The U.S of course, while "extremely disappointed", won't oppose the popular will of the Taiwanese people.
And that's how the U.S abandons its ally without abandoning its ally, and China takes Taiwan by force without ever firing a single shot.
Of course, that's just one possible scenario out of thousands. The question here is intent - if the U.S intends to fight China it will for its own purposes. if the U.S doesn't intent to fight China it won't for its own purposes. Countries aren't as beholden to their public image as people think, because there's a million ways to spin anything.
To your other point: I have traveled to Taiwan 6 times in the last year (going again in Feb.) It is quite clear there is close to zero support in the population for reunification under current Chinese (mainland) system. This is not to say there is no support for being part of China again - just not as it is today. If the government of mainland China became an full Democracy however it is clear this would happen.
I agree that the US people are mostly not interested in being an empire, and massive economic disruption plus high casualties would mean a very very unpopular war.
Don't get me wrong, a US-China war would be absolutely catastrophic in both humanitarian and economic terms, but the average US citizen wasn't exactly starving even during WWII. Unless the war seriously damaged domestic infrastructure, (which it very well could) people would get by with ration coupons and price controls.
[1] http://www.fool.com/investing/general/2014/01/12/will-the-un...
As a general rule of thumb, that's not true. From time to time I work with merchant shipping, particularly in times and areas of serious risk (such as warzones) and they don't stop. They happily traversed the straits of Hormuz while missiles were being fired across it. They kept serving Libya during the civil war, with shipping companies literally calling ahead to check which port to head for. They won't stop unless someone starts attacking them specifically, and even then they'll just be going around. China doesn't have the global reach to threaten shipping beyond what is, on the global scale, a small range, and threatening the shipping in their own waters would harm them more than anyone else.
How will that play in Tokyo or Seoul? Or hell, in London or Jerusalem?
If the US does go to war over Taiwan, it will be to maintain its credibility with international allies.
Korea and Japan are largely safe because there's a massive US chip on the table. Ditto the minor Southeast Asian powers. If the US doesn't come to Taiwan's aid in a shooting war, that chip is now off the table and China will have free reign to do whatever along the Pacific Rim with impunity.
Now, whether or not domestically it would be a good idea to get into another war (with China at that) is a whole 'nother story. But in terms of regional stability, there are many good arguments for intervention.
So what? The intermediate term impact would be massive capital flight to the Americas. Asia as a reliable place for manufacturing would be over. Americans would think hard about what's really at stake.
As a superpower the US's interests are necessarily long-term, strategically. Sure, the immediate reaction of China jack-booting all up and down the Pacific Rim would be economic and political turmoil. It's the long-term possibility: Chinese hegemony over the entirety of the Pacific coastline, that scares the shit out of the US.
Bear in mind that the USSR, despite not being an export power (like, ever) was still able to pose an enormous threat to the existence of the USA. China losing its preferred-manufacturer status wouldn't be consequence free, but it also wouldn't de-claw them.
I doubt there is an American naval battleplan more developed than China attempting to cross the Taiwan straight. China's hopes rest more on missile attacks on Taiwan forcing surrender than an invasion. Subduing populaces by ariel attacks is surprisingly hard and counter productive, and nothing is more likely to turn pro-China Taiwanese away from their views quicker than that.