Sorta-kinda. It’s complicated.
Vietnam, the US, the Philippines and others have clashed with China over the “Nine Dash Line.” China— and Taiwan, oddly enough— refuses to respect the ruling of the UN Convention of the Law of the Sea (UNCLOS) Tribunal on this matter. They’ve harassed other countries’ fishing vessels and maritime police in the region, sinking at least one. There are ongoing tensions in the area between China and other countries’ navies. China asserts sovereignty over almost the entire South China Sea, while other countries and the UNCLOS disagree and assert their right to freedom of navigation for military vessels. This has implications for customs and maritime law enforcement.
https://www.theguardian.com/world/2014/may/07/chinese-vietna...
Some people in Taiwan might be willing to give that up in exchange for a guarantee of independence but as far as I know this is not at all a settled matter for them. It’s very much like North Korea/South Korea.
China does not object to transit through the South China Sea. China objects to foreign military vessels entering into the territorial waters within 12 miles of what it considers its own islands. The US and its allies conduct these "freedom of navigation" operations explicitly in order to challenge Chinese sovereignty over said islands and reefs.
But what you're discussing here is sovereignty over a certain set of islands and reefs that China (and several other countries) claims, not freedom of navigation through international waters.
China's aim is, quite clearly, to prevent the US Navy from operating in the South China Sea in the case of a war. That's not a question of freedom of navigation, and the US "freedom of navigation" operations have to go out of their way to go near the islands China claims.
China is additionally interested in the resources under the South China Sea, just as all the other countries that occupy various islands and reefs are. This, again, is not an issue of freedom of navigation.
China isn't about to block shipping through the South China Sea.
As for freedom of navigation, China is also in favor of that. It's their lifeblood.