I mean the war is effectively over. It's been a cold war since the "cease fire" has been adhered to. It's not like they're going to stop trying if we agreed to take down the DMZ. Their entire culture is based around reunification and defeating the evil Americans.
Less flippantly, "ending the war" means reaching a mutual agreement that preserves the two Korea's current territories: nobody sane is using the term to mean anything else.
(BTW, South Korea did push for officially ending the war multiple times, IIRC. It's just that North Korea remains uninterested. Same for the US - probably because they don't see the deal happening realistically.)
Could you elaborate on if you genuinely think this would resolve the issues the DPRK experiences?
Takes two, not just the UN side, to end the war.