To circle back, the original comment was that PRC claims had no legitimate basis in history and law. I pointed out ROC claims were based of both law and history, with enough tacit endorsement (by security members and other claimants) at the time that in terms of consensus, Chinese claims constitute the oldest and strongest among all claimants. Which is true. PRC inherited these claims, and the argument has not changed, only the geopolitical context has. Especially post UNCLOS when ownership granted EEZs and other territorial perks, and now SCS SLOCs and resource claims.

>Of course it matters how good their argument is – if it was stronger than enough countries would be interested in maintaining stable international order to back them up.

No international actor wants a regional Asian hegemony except China, there's no argument strong enough to override such interests. And there's no argument strong enough to form consensus among 6 claimants or US desire for Chinese containment. SCS is simply not a dispute that can be solved legally / multilaterally anymore, unless bilaterally under Chinese terms like original UNCLOS accession conditions. In the meantime, China has the industrial capacity change the conditions on the ground. Probably the most expedient method now, hence arguing over claims is not productive. The claims exist with clear historical documentation, for pretense of Chinese enforcement, that's all that matters.