The ultimate concern is the lives and property of the South Koreans. Our troops could get through the barrage, but may only be capable of a limited response considering all of the civilians South of the zone.
While our troops could get through a lot of the ensuing bombardment and respond, there's nothing that could make the whole of South Korea bullet and bomb proof. The entire South side up through Seoul would be a series of large craters. Perhaps then their youth would begin to understand why we are there to begin with? Wouldn't matter. Once both sides are devastated, China sweeps in and makes them both a poor Eastern province.
I think you're right. China certainly is going to be the King od the East one way or another.