I think China would much rather take Taiwan in 10 or 20 years than today, and it would take some serious goading to spark an actual conflict. Could they pull it

I think China would much rather take Taiwan in 10 or 20 years than today, and it would take some serious goading to spark an actual conflict. Could they pull it off today? I'd give them decent odds, but as you describe, even the best case would be painful and expensive. Opposed amphibious landings are extremely hard to pull off. In terms of public opinion, I think you underestimate the extent to which Chinese people believe that Taiwan is a rightful part of China. Their domestic audience would not view it as invading another nation, but rather the rightful culmination of a long effort to reunify territory lost during the century of humiliation (eg. Hong Kong, Macau). Biden's statement that the US would defend Taiwan was an unscripted gaffe in response to a question that the White House walked back within hours. In reality, the US has no legal obligation or treaty compelling it to defend Taiwan. Again, there are pretty clear parallels to Ukraine, where the US provides materiel and support, but isn't willing to actually guarantee military intervention. My takeaway is that this visit will ratchet up tensions and has a very small probability of escalating into a serious crisis, for no appreciable foreign policy benefit. It just looks like a cynical attempt to shore up foreign policy weakness before the midterms, after the mess in Afghanistan and Ukraine.