The problem of US forcing SK to join the war is what if North Korea joins and what is the off ramp for North Korea?
If SK loses to PRC, is SK going to get absorbed by NK? That would be a huge humanitarian disaster affecting everyone in that region. Huge quantity of refugee will flee to Japan or even China if they are desperate.
What if SK concedes to PRC but continues to fight NK? That would be a bigger death toll that armed reunification. One is a naval/air battle, and the other land battle.
If SK wins, will NK use nuke as the last resort for the political regime to survive? Neither PRC and US can control NK in that regard. There is a history of SK presidents want to be the named "The unifier," they would definitely want to push for reunification after a hard fought war, not another armistice.
If NK joins, is PRC going to start a land war through the peninsula? That would rapidly favor PRC and NK over SK and USFK.
Or does PRC even want a unified NK or SK? For sure not unified SK with US bases but I feel like PRC enjoys the best of both worlds by having both of them. One great trade partner and the other is a great shield.
These are just some situations I can think of, there are plenty of other situations for sure, and plenty of in between situations. But I think people in this thread forgot how hard is to offramp North Korea once they join in the fray compare to US/PRC/JPN.