Some historians believe that by 1945, we would have started to run out of men who would make good soldiers, maybe we were close to being bled dry. The UK was much worse. If that was the case, we had to bring the atomic bomb into play.
The big worry, too, is that with a seriously weakened fighting force and the utter chaos in Japan that the invasion would’ve brought, the Soviets would’ve just sauntered in and taken over to establish another Communist state. In turn, there would’ve been no way for us to have challenged the situation in Korea shortly after, either. The entirety of Asia would’ve fallen like dominoes to the forces of darkness.