It might, probably would have, but politically that would be a tough sell to an American public that had the horror of WWII fresh in everyone's mind plus having fought the Chinese to a draw only one year prior. IIRC the sitting president got his job partly on a campaign promise of "going to Korea" to end that war. Not a good idea to risk or even to be seen to risk starting another one a year later.
Gunnery, gunnery, gunnery. Hit the target, all else is twaddle!
