Americans seem to be proud of their participation in the war.
That's kind of a harsh way of putting it, but perhaps it's not inaccurate. While we like to try and deny it (primarily out of our misplaced desire to try and make European countries feel that we're more like them, a centuries-old tendency which is thankfully beginning to fade), but America, like Catherinic Russia, ancient Sparta or Feudal Japan, is very much a martial society. We consider service in wartime to be a mark of courage and indeed elevate it to one of the highest honors that one can achieve.
With that said, the Korean War was a mess. Going into it was absolutely necessary, but we went in against China (who had maintained their standing army from WW2) and Russia (who had maintained their standing army from WW2) with a military force we had largely dissolved after WW2. In an attempt to try an compensate for this, we got the UN involved, but that became the same administrative disaster it always has been. Also, our leaders foolishly trusted that China would remember how we saved them in WW2 and not rush into battle against us, in which case we were sorely disappointed.
The biggest failure of American policy in the Korean War was a refusal to acknowledge that it was a war and declare it so. As it was, we wiped out 800,000 Chinese troops at the loss of 33,000 of our own (I don't have accurate statistics for how many Koreans died on either side of the line) and kept the Chinese empire from finishing Mao's vision of making Korea a neo-tributary, so it goes down as a "Victory" but it was not a complete one. Had we actually declared it to be a war, and not a "police action," and treated it with the same gusto we treated WW2, the Kim regime would never have taken root and Korea would be united today.
On the other hand, China would have viewed a united Korea (with American leanings) to be a constant threat for the next 70 years and would almost undoubtedly have launched some kind of campaign against Korea (probably driven by some moronic nationalism and the claims that Korea belonged to China because some ancient dynasty held it as a tributary), so maybe it is actually better that we settled for a "that side's yours and this side's mine" ending.