The U.S. has never been the world leader. The U.S. has been a military leader for other democracies since the end of WWII. That is why the title, leader of the free world has been applied to the U.S. president, who is the leader of the various military alliances between various major democracies. If you claim the U.S. considered itself to be the world leader, then you are claiming the U.S. considered itself to be the leader of the Soviet Union, the Warsaw pact, North Korea, etcetera. That is absurd. The U.S. likely did consider itself the leader of Vietnam and Cuba before the democracies in those countries fell, although that was in a military capacity. That is why the U.S. intervened militarily in both, although both interventions failed.

Saying that the U.S. got its leadership position because no one else wanted it is historically incorrect. Following WWII, every other major democratic power was in ruins while the U.S. was the sole major power left in tact. Without any military attacks on U.S. soil, U.S. military strength had skyrocketed during the war. As the war progressed, the U.S. attained the status of a great power and by the war’s end had become a nascent super power. U.S. strength continued to grow after the war due to the threat of the Soviet Union. Meanwhile, the other great powers never fully recovered militarily since they focused on their economies while relying on the U.S. for security. The U.S. gained its leadership position because no one else existed that could claim it.