It wasn’t a matter of not finishing the job, more MacArthur crossing the border into China, China responding with greater numbers than 'UN' forces could counter, leaving us with the choice between going nuclear and accepting some kind of stalemate. Bear in mind that there was a massive demobilization post WWII as we were suffering under the misapprehension that 'nukes made armies obsolete'. We still had a capable navy IMO due to Bretton Woods, but that made it more about overwatch than power projection - and this was very much a land war. That war, and the cold war in general is an interesting period.