What makes you think the Chinese are really that interested in projecting naval power a great distance from home? They don't need to do so in order to achieve hegemony in Asia.
Them being able to control their littorals (and yes, it would be a bloody mess for the US to control anything within shore based missile range of China) is useful for immediate defense, but no realistic US strategy against China would call for us needing to control those littorals.
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