We have more superhero war movies this century than ones for this.
In the past, the problem was timing. The Korean War came on the heels of the WWII, and people were tired of war. Movie studios would have had a hard time selling movies about a new war to people who had only been home from the last one for five years. Most of the films made about the war were on the exploitation side. Then, before the dust could settle in Korea, America Tarzan-swung balls-first into the even bloodier Vietnam War.
But today there is a much different problem: China, which has become a huge market for the film industry. And the Chinese government has made it clear that they want more positive representation in movies if Hollywood wants their money. American studios want to avoid portraying China as bad guys to make sure their films play globally. The issue with making a Korean War flick is that China fought alongside North Korea, and still has a somewhat supportive relationship with them. Studios don't want to risk losing the money they'd get from Chinese ticket sales of Transformers 9: Shia's Revenge.