For the Japanese and Koreans, yes, the SCS is important, but hardly critical. Worst case, their ships can loop around the Phillipines east coast and approach from the west. It will add time and cost, but not prohibitively.
For China, if a foreign power controlled the SCS, they can effectively cut Chinese sea based trade lines.
Chinese shipping cannot loop around the same way, as that would be putting them further into the reach of likely hostile foreign powers.
The SCS is the only place on earth where such a blockade would have any hope of succeeding.
Further away and you cannot easily distinguish who’s ships are sailing and where they are going, especially if those ships are actively trying to hide their identity and destination.
Closer and you run into practically and cost barriers as trying to conduct an interdiction campaign within range of mainland Chinese air and land based assets is going to be extreme costly, if not downright impossible.
So, for China, the SCS is effectively an existential issue.
No other power has that level of commitment to the issue, or that resources that could be brought to bare to defend it.
That is why the whole FONOP business is just a non-starter. If push comes to shove, China has the means and motivation to go as far as needed to win there. Whereas no other power can have such commitment or capabilities to wrestle control from China at this point in time, never mind the future.