Or, if Taiwanese or American resistance is stronger than expected and Chinese power weaker, China can walk back the crisis without having actually risked all that much.
From a military perspective, your analysis makes reasonable sense, however, it's excluding two major considerations:
1. Taiwan may try, and almost certainly has already prepared, a 'cause disproportionate damage while accepting loss of the islands' strategy. Prepared minefields, drone bombs, some deep bunkers, and ready evacuation plans, allowing the Taiwanese to bloody the nose of a landing force before retreating swiftly. If they're willing to do it, some cheap tube artillery set up to counter-shell before running.
With the Wuciou island in particular, there isn't really any other reasonable defensive plan, and critically, China is extremely unlikely to be able to conceal a military build-up for invasion. Wuciou is small enough that maybe a small task force could be stealthily gathered for that, but either of the larger island sets, it's not practical, so Taiwan would certainly see the invasion coming.
2. The worst-case scenario for the CCP/PLA isn't direct US military involvement, it's interdiction of trade. The PLAN has effectively no ability to resist the USN out on the high seas, and China's economy is both dependent on exports for what sectors aren't Ponzi schemes,
and dependent upon imports to
feed itself. If the USA declares 'All maritime trade to and from China is hereby interdicted until they retreat from Taiwanese soil,' not only will a lot of regional allies and frenemies enthusiastically back the declaration, there's jack-all the Chinese can do to overturn that declaration.
While the loss of export markets would be hard on some places like Australia, many friends would be made by the interdiction of and sinking of the Chinese pirate fishing fleets. Food and energy shortages in China would start within weeks, and become acute within months. They can bring in
some stuff from their Belt-and-Road, but that hasn't worked anywhere near as well it was supposed to, and it was
supposed to replace maybe a quarter of maritime trade volume.
China would probably have 3-6 months before economic collapse, and that's optimistic. If one of their
many fracture points shattered as a result of naval interdiction, you could see cascade economic failures a lot faster than that, and if a sizable chunk of the military is already deployed fighting Taiwan, who knows what kinds of insurrection might happen?
Further, since naval traffic to and from China primarily goes through the territorial waters of nations they've pissed off, such as the Straits of Malacca, which are
extremely easy to close, and China can't force to open without declaring war on additional nations. If China wants to try to use the small portion of the PLAN capable of long-range blue-water deployment to send merchant shipping convoys around through open waters, they pretty much have to go all the way around Australia, adding thousands of miles and weeks to the journey. It's logistically impractical, and certainly can't handle even a fraction of the shipping volume currently going in and out of China.
On the whole, between China's incredibly shitty diplomacy with literally everyone in the world, and how economically exposed they are, their most practical option is basically to try what the Russians tried, and hope they actually succeed. Try to start and then
win the war before western governments manage to respond coherently, so it's functionally presented as a fait accompli. 'We already have Taiwan, what are you going to do about it?'
They're even less likely to succeed than the Russians were, to be frank. It's not impossible, and it's not impossible that they'd try a more gradual conflict process like you're proposing, but given how politicized and inexperienced the Chinese military is, it's extremely unlikely they'd try something that sophisticated.
Far more likely they'll try the overwhelming blunt force method, and break their teeth in the process.
