McArthur's comment is true today. For example, Japan went to war with the US over oil in WWII. It is more dependent on Middle Eastern oil today than it was in the 40's.
So the probable result of Chinese occupation of Taiwan is neutralization of Japan, Korea and the Phillipines. With that one stroke, China will have eliminated all locations from which western air assets may be conveniently deployed against much of China.
Sure, the public in China has been whipped up into nationalist pride and I do not discount the importance of pride in sustaining popular support for a policy. But the leadership would not be investing the billions it has put into arming to invade Taiwan (nor would it spend countless dollars whipping up that pride) unless Taiwan were so strategically important.
I don't discount the strategic importance, but "neutralization", whatever's meant by that, is likely gong to take more than proximity to "preferred" shipping lanes. Without more evidence of that as a motivation, I dont find your argument convincing. Nations have invested a more for less strategic ambitions, including our own.