Why do the United States and its allies allow Communist states to exist?

You have a very simplistic view fo the world and an overreaching view of the power of the military of the United States, without the use of nuclear weaponry! First, look to Africa. There are many evil governments in Africa abusing their citizens. The corruption of government in African nations is legendary, and the leaders are filling their Swiss accounts with billions as the people starve. What could the United States do? We could easily invade these nations and seize control of the governments with limited casualties (perhaps less than 1,000) but then what? You cannot just build a nation out of nothing. There must be a tradition of self-government, a system of law, a system of courts, and infrastructure, and so much more. Sure, if the United States wanted to face tens of thousands of deaths most communist nations (other than China) could be invaded. Then what? The United States cannot police the world. Have you heard that we are out of money and also the populace is very "war weary." No, you cannot look at the world in the simplistic terms you have outlined in your question as though this was a game of "Risk" and you are moving pieces around the board of the world. The world is an evil place. Governments are repressive and corrupt. Millions of human beings are suffering. All of this is true. Now what?