What is the accepted procedure for setting an ADIZ? Large scale US and Russian naval and air exercises are common, they often involve a lot of airspace beyond national territorial limits, how is that handled? If there is lots of precedent for such requirements made by other forces during exercises, it will be hard for the US to object to China's doing the same.
Obviously the Chinese protests are because they hope to gradually get de facto acceptance of their territorial claims by setting up ID zones, anticipating that traffic has to conform to Chinese regulations. This seems like a low risk approach to building sovereignty.