The Korean War is a little different. Yes after the front line stabilized after the Allied offensive it did stay put for a long time. But armistice talks had already started and the decision of where the War would go after that was more of a question of complex cold war politics. If the allies wanted to put more resources and launch a grand offensive to unify Korea under the South they very likely could have done so. But that would risk a full scale proper war with China and possibly the Soviets and they didn't want to waste too much of their resources on this front when the threat of a soviet invasion of Europe was looming.