The larger question is why did the Taiwanese even suggest this as an option? Certain Taiwanese people were saying two missiles can do the job They could have consulted their own civil engineers and came to the same conclusions.
A belief that they hold an advantage over China makes it easier to spend less, have slipping defence programs and not push harder on conscription. To the casual lay person, it seems plausible. It wasn't Taiwans only card, their is also this belief that their strategic industries will mean China won't attack them, and the US will absolutely come to save them.
The US has the capabilities to damage this dam, but would have to assert massive air superiority over mainland China, not exactly an easy or cheap thing to obtain. Even then, it would be seen mostly as a civilian target, with a massive civilian casualty.
Taiwan doesn't have to defeat China is a straight up one on one fight. It just has to have significant capability to deter. Russia invaded Ukraine, because Ukraine politically & military was judged to be a soft target that Russia could win. Embolden by their previous efforts, the expected the whole country to fail to defend itself and it would be easy to make crushing victories like taking the capital, at which point there probably would be no organized military resistance.
China does not feel its current military capability is enough to comfortably take Taiwan. But in less than 5 years that is likely to change, as China seeks very near parity with the US, and Taiwan's capability continue to be fairly weak or age and erode.
We can see the US and Japan have concerns, because the US is significantly upgrading Guam, and Japan is significantly upgrading its lower island defences. Neither of these locations will be able to entirely defend Taiwan and stop an invasion, but they would be key locations in an prolonged fight to resist invasion. It is unlikely China would want to expand the fight to the US or Japan, and it would seek to deter both of them from getting involved in "an internal Chinese issue". It intends to take Taiwan, and keep others away,
The Americans aren't going to fight and high intensity war with China directly, just to keep Taiwan free and back up its minimal defence spending. That didn't happen in South Vietnam, it didn't happen in Ukraine. Sure they will supply weapons and intel, they might even distract and keep some Chinese forces busy. But ultimately the fight for Taiwan need to come from the Taiwanese themselves.
If China attacks any us bases or tried to limit their capability, well Pearl Harbor all over again and that will definitely be a US v China. So China is likely to be very careful to keep the Americans at bay. They may be a bit more direct with the Japanese.
But as we have seen in many recent conflicts, its an assistance, not completely handling the problem themselves. If you look at South Korea which faces a huge land based threat and even less strategic depth, they are in a much better position to defend themselves, and seem to indicate they would be able to sustain a resistance until a bigger US and global allies effort came to settle that game. South Korea does have similar issues with weapons and conscriptions, but they seem to be at a far higher order of capability. Taiwan has a fairly high GDP particularly PPP, and a reasonable population size. It isn't as tiny in size and population as Singapore, and it isn't exactly poor either.
Taiwan needs to address their weaknesses with great energy. At this stage, there isn't much time to bring in new platforms, but munitions and turn key weapon systems are still possible. An intensive call up of recent past conscript and addressing the current conscription system could easily turn around the training issues they have. Politically not popular, but it is time to start being realistic.