So, if the USA had had a third bomb, then they would have been required to drop it on Japan so that the World could see that they had more than two bombs, I suppose...?

After all, are 2 measly little A-bombs really enough to sufficiently impress the World (and the Russians in particular)? They only dropped 2 because they only had two to drop. Japanese lives were not considered very valuable at the time. Matter of fact, I believe they were hardly considered to be human at all by a lot of westerners.

Fortunately the Emperor of Japan took it upon himself to make the decision to end the fighting. Good thing. The Army generals were less sensible than he was.