You have a very mistaken view of the Cold War. It was not an effort "to eradicate communism." It was a result of a perceived shift in the balance of power between the USA and the USSR after World War II. It had various phases and stages in both US and Soviet thought, and that balance was not static. But the general US goal was to prevent Communism from spreading, which is not the same thing as eradication at all.

One might ask whether the Cold War "truly" ended, and many have. The US-Russia situation is not as rosy as people thought in the early 1990s. And while the question of whether China is Communist or not is debatable (they are authoritarian but their economy is not obviously Communist anymore), they have certainly emerged as a great power rival as many predicted.

But you should be clear on the issue that the US goal was never to eradicate Communism. It was to increase the American sphere of influence and try, as best as possible, to contain or decrease the Soviet sphere of influence without the breakout of general war.