As mentioned elsewhere in this thread, I used to think it was inevitable that China will be able to successfully invade Taiwan, but its almost impossible to pull of an amphibious invasion. Taiwan's geography makes this particularly difficult.
No power has attempted to sink a carrier since 1945, there is ultimately limited data on how effective any anti-carrier weapon developed in the last 80 years would be in practice.
Saturation by long-range antiship missiles is also possible to work, if the Falkland War is any indication.
And then there are the "deorbit a tungsten telephone pole" kind of ideas that just might work on a carrier, have no defense and are within the realm of possibility for both China, Russia and basically every state with the capability to get a few tons into some low orbit.
Against sophisticated enemies, carriers are giant billboards with "shoot me" written on them.
Italian battleships were targeted & 3 were disabled.
Also the British tried to sink the Argentinian aircraft carrier during the Falkland War and it escaped preatty much just due to luck.
The schools used to have duck and cover drills to prepare for nuclear attacks. This may have made people too afraid of the word nuclear and thus nuclear power is not possible in the US. Now there are "stranger on campus" drills instead. I wonder how that is warping the minds of the present generation.
On average I feel rather unimpressed by that threat. It seems like a conditioning.
If you read my second statement, I do agree with you that great, unreasonable fear can be conditioned into people. This is what happened to the word "nuclear". The reasonable fear of nuclear weapons got put into children in the 1950's, but being children they just ended up fearing everything nuclear. And being normal humans almost all did not evaluate new evidence in adulthood and change their minds. These people are the Baby Boomers that have controlled society for a long time and have let coal plants exist for 50 years do huge environmental damage, while relatively clean nuclear power was abandoned.
P.S: The radiation from these bombs are not the problem, it is the nuclear winter that is.
The waters of the strait are also shallow enough that submarines are not that effective.
Basically, it is certainly possible to pull of such an amphibious assault, and the US Navy's simulations recognize as much.
That is the hard part. Not only would you have to deal with US carrier based air assets, but also air assets from bases in Japan and South Korea. In addition, Aegis based cruisers also have a heavy anti-aircraft armament.
As for Japan, it is much too far from Taiwan to contribute. South Korea will not get involved for obvious reasons.
They don't have to immediately pull off an invasion. Tomorrow they could begin a draconian blockade, while strategically bombing the island and begin an assassination & disruption campaign by inserting special forces. They can do it (rather inexpensively) on an indefinite basis, as long as they care to. Nobody can stop that and they have zero concern for the humanitarian disaster it would cause, with their eye on the long-term goal. Taiwan wouldn't last very long in that simple and very obvious scenario, it would rapidly degrade their condition. The world (those standing opposed to China's move) would quickly capitulate, understanding full well that the alternative is all out war with China; the UN would be begging for a settlement peace within weeks (which would result in China de facto taking over Taiwan). Mostly all that would happen to China are some sanctions, which China would shrug off (along with some dramatic, harshly worded PR releases). At the end of it, China won't need to invade with a large amphibious assault, it'll enter Taiwan largely unopposed as part of the brokered peace settlement.
China is very rapidly building up its naval capabilities. It will be able to invade Taiwan this decade. That isn't a maybe, it's a certainty.
Even more effective for China is to simply invest a few billion Dollars into bribing politicians. Some would argue that this has already been done with the KMT. They can also put pressure on the owners of the first generation of factories in China, which tend to be related to KMT. They will give up Taiwan in order to keep their business.