I've never understood this argument. South Korea is already a US ally, and I don't see how the land of North Korea is more strategically beneficial than South Korea already is. It's not like the US needs to be directly bordering China to be able to launch missiles there or to spy on them.

I think you are right that there is a "prestige" factor to this as well. China doesn't want to lose an ally, regardless of whether having that ally benefits them much, because they would look weak backing down to the US.