It was not impossible for capitalist and communist governments to work together after World War 2. In fact, there were several instances of cooperation between the two sides, most notably the formation of the United Nations in 1945. The UN was created as a way for countries to resolve disputes peacefully and to promote international cooperation. It has been successful in preventing several major conflicts and has played a vital role in promoting development and human rights around the world.
Additionally, there were several other examples of cooperation between capitalist and communist governments during the Cold War. For example, the United States and the Soviet Union worked together to resolve the Cuban Missile Crisis in 1962 and to negotiate several arms control agreements.