They'd absolutely intervene, given the economic ties and political prestige attached to Taiwan, but then we would rapidly get our asses kicked. Don't believe me, believe the Pentagon:
The U.S. Military 'Failed Miserably' in a Fake Battle Over Taiwan
The U.S. military reportedly "failed miserably" in a series of wargame scenarios designed to test the Pentagon's might. The flunked exercises, which took place last October, are a red flag that the way the military has operated for years isn't going to fly against today's enemies.
Specifically, a simulated adversary that has studied the American way of war for decades managed to run rings around U.S. forces, defeating them decisively. "They knew exactly what we're going to do before we did it," Gen. John Hyten, Vice Chairman of the Joint Chiefs of Staff,
revealed at an industry event.
While Hyten did not disclose the name of the wargame (it's classifed), he did say that one of the exercises focused exclusively on a brawl between U.S. and Chinese forces fighting over Taiwan—a scenario that seems
increasingly likely.
'We're going to lose fast': U.S. Air Force held a war game that started with a Chinese biological attack
Meanwhile, a leading Chinese think tank recently described tensions in U.S.-China relations as the worst since the Tiananmen Square massacre in 1989, and it advised Communist Party leaders to prepare for war with the United States.
What many Americans don’t realize is that years of classified Pentagon war games strongly suggest that the U.S. military would lose that war.
“More than a decade ago, our war games indicated that the Chinese were doing a good job of investing in military capabilities that would make our preferred model of expeditionary warfare, where we push forces forward and operate out of relatively safe bases and sanctuaries, increasingly difficult,” Air Force Lt. Gen. S. Clinton Hinote, deputy chief of staff for strategy, integration and requirements, told Yahoo News in an exclusive interview. By 2018, the People’s Liberation Army had fielded many of those forces in large numbers, to include massive arsenals of precision-guided surface-to-air and surface-to-surface missiles, a space-based constellation of navigation and targeting satellites and the largest navy in the world.
“At that point the trend in our war games was not just that we were losing, but we were losing faster,” Hinote said. “After the 2018 war game I distinctly remember one of our gurus of war gaming standing in front of the Air Force secretary and chief of staff, and telling them that we should never play this war game scenario [of a Chinese attack on Taiwan] again, because we know what is going to happen. The definitive answer if the U.S. military doesn’t change course is that we’re going to lose fast. In that case, an American president would likely be presented with almost a fait accompli.”