The United States, T. R. Fehrenbach explains (in This Kind of War), had to continue to defend South Korea, while at the same time consolidating the defense of Europe:
The major potential foe was still Soviet Russia, and Europe still the world’s great prize. Any measure that provided relief for the United States forces in Korea, but set back United States support or strength in Europe, would be imprudent. If the United States began a unilateral war with Red China, it stood an excellent chance of fatally rupturing the embryonic North Atlantic Treaty Organization which for some years had been a goal of its policy.
MacArthur was told to hold the frontier so that the tribes of the interior could continue to organize, and to forget about carrying the war to the barbarians.
[...]
America had the bomb, but no divisions. There was no barrier in middle Europe that could prevent its being overrun by the massive Red Army.
Until such a barrier could be built, under NATO, Washington would never breathe easy. It would never favor involvement in Asia. It would continue to eye such involvement suspiciously, looking for a Russian trick.