Since a treaty has never been signed and an armistice concluded the war in 1953. War is technically still going on between the two counties. Would the signing of a treaty end the hostilities between the two?
But the thing is... a peace treaty won't be signed until hostilities end. The chicken and the egg.
^ That and the fact that the two different systems and regimes will always despise each other and guard against a future attack. The status quo is beneficial to SK since it allows more US support than would be present under a peace treaty. There will never be a peace treaty with the NK regime.