I'm guessing the issue is that NK is an openly hostile country that is not only threatening its southern neighbor but also the region.
India and Pakistan may have a beef with each other, but they weren't a destabilizing force in the region, or maybe more accurately, if they were, it wasn't a huge concern of the superpowers at the time.
NK v SK conflict is not that different to India v Pakistan. The difference is... there are US troops sitting on the border of NK/SK, so agression between those to parties involves the US.
So who is the destabilising force in the region? I'm pretty sure "stability" isn't the goal (for the US) it's "Democracy".
The difference is so much greater than that. North Korea is a completely irrational regime. It is lost in a fantasy world. Pakistan, though it's stability is questionable, is not off on some bizarre ideological island. It's not as if the Pakistani government could convince it's citizens of the sort of nonsense the North Korean government does.
India and Pakistan may have a beef with each other, but they weren't a destabilizing force in the region, or maybe more accurately, if they were, it wasn't a huge concern of the superpowers at the time.