“The U.S. would almost immediately achieve air supremacy. And that’s pretty much all she wrote, these days.”
I don’t think the Chinese air force would be a match for ours, and we would have pretty strong air superiority, but I wouldn’t say we’d necessarily have air supremacy. Though the North Vietnamese fielded a tiny air force, they managed to throw up some decent anti-aircraft at our bombers over Hanoi, enough that a bombing mission was NOT a “you push the button, we do the rest” exercise. (Ask Senator McCain.) And with American pilots in enemy hands, the reason for the war comes into the picture. If we were pissed at the Chinese for some terrorist or Pearl-Harbor-style attack, having our pilots in enemy hands would only stiffen the American people’s resolve. But if it were a war over Taiwan or something that the home crowd doesn’t feel THAT strongly about, the prospect of long and painful captivity for the bomber crews would cause the public to call long and loud for a quick end to the war to bring the prisoners home.
As to comparisons between a hypothetical war with China and the Gulf War, just remember that Iraq had to buy its tanks, rockets, etc. from other countries, while China makes its own. (In fact, China probably supplied a lot of Iraq’s weapons in the years before the Gulf War.) That makes a BIG difference in how long the Chinese could maintain a war effort compared to the Iraqis.