If China can take out CSGs with pretty much no effective counter measures, will the US be willing to send carriers to support Taiwan during/after a Chinese inva

If China can take out CSGs with pretty much no effective counter measures, will the US be willing to send carriers to support Taiwan during/after a Chinese invasion? It's all a game of brinkmanship - might be time for US/China to dig out the old Cold War doctrines on how to win a conventional war without winning so hard the other side feels the need to start slinging nukes.