I think you have the issues backwards. The US is not opposing the claims by China but rather the view that it should clarify its claims and the legal basis for it. Sovereignty is the root and underlying foundation from which all other issues emanate. The central premise is, does China have sovereignty over those rocks and accordingly what jurisprudence rights emanate from it? If China indeed (not proven) has sovereignty over them, then every other state including the US has to deal with that legal reality, regardless of FON. Unfortunately the claim by China is disputed by other interested parties. Secondly, the claims affects FON depending on whether it is an island, maritime or some kind of historic claim which China is rather unwilling to lay out its case beyond mere statements of sovereignty. Since China is not forthcoming with its basis, my read is that the US will challenge the claim via FON and will make incursion into the zone on the basis that sovereignty is disputed and hence not recognized until the matter is resolved.
Such a position I could accept, if the US were equally concerned with every territorial dispute in the world and willing to challenge everyone's claims via FON or equivalents.
However from what we can gather the US seems to be quite interested and involved in China's involvement with its territorial disputes in the SCS while far less involved in other disputes around the world or even the region, with seemingly little clarification sought in most of those disputes.
So, if you agree that the US seems to be particularly interested in China's specific dispute at this area compared to other regions of the world, the next question one has to ask is why?
Furthermore, do you believe that the US would accept China's position on its territory even if China clearly stated and cease conducting FON simply on the basis of a clarification? I imagine if China's clarification was detrimental to US geopolitical and military interests the US would continue challenging or even increase the intensity of the challenges.
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Edit: you also say sovereignty is the root and underlying foundation of all issues, but that's only half the story. The US is interested in the sovereignty of the matter and interested in challenging the sovereignty not because of the nebulous concept of sovereignty but rather because there are material capabilities, abilities and geopolitical advantages that sovereignty can entail. The way I read it, the root issue is power and ability to project power over the SCS.