The U.S. doesn’t claim the sea as its sovereign waters. China does. (Which had the totally unpredictable effect of majorly pissing off every one of its maritime neighbours.)
There are disputes over territorial waters and EEZs. China uniquely claims the whole damn thing, not as its exclusive economic zone, but its sovereign territory. The Philippines aren't asking for the right to tax ships passing through its EEZ, it just wants to fish and drill and mine them.
Source? I've never heard of Taiwan claiming waters off the coasts of Brunei, Malaysia and Vietnam as China does [1].
[1] https://en.wikipedia.org/wiki/Nine-dash_line#/media/File:9_d...
In fact, the famous "dashed-line" claims in the South China Sea were originally made by the Republic of China, before it was defeated by the Communists. This is a map from 1947, showing the ROC's eleven-dash line: [0].
The only difference that I know of between the claims of the ROC and the PRC is that the PRC has slightly reduced its claims as a result of an agreement with Vietnam over the naval boundary in the Gulf of Tonkin.
0. https://commons.wikimedia.org/wiki/File:1947_Nanhai_Zhudao.p...
Taiwan doesn’t assert the claim [1]. There is sensitivity around explicitly abandoning it, as “changing the ROC’s historical claims would indicate—especially to Beijing—that the island democracy was abandoning its historical political identity and moving towards an inherently Taiwanese national identity, or even independence” [2]. To the degree Taipei has legitimately aligned with Beijing, it has been in the limited sense of arguing Taiwan is legally a real island, not an islet which cannot make any maritime claims [3][4].
[1] https://www.taipeitimes.com/News/front/archives/2016/07/15/2...
[2] https://globaltaiwan.org/2020/07/taiwans-delicate-balancing-...
[3] https://focustaiwan.tw/politics/201607120024
[4] https://www.forbes.com/sites/ralphjennings/2016/03/23/how-ta...
Tsai Ing-Wen doesn't want to look like she's aligning herself with China on this issue, but this is long-standing ROC policy, going back to before the PRC was even founded. It's not something the PRC invented.
just cause a sea is named after a country doesn't mean it's theirs
just like Sea of Japan