Hindsight is 20-20 as they say. The problem with this theory is that in 1945 our military intel people couldn’t sit down and interview Japanese leaders. There was a war on, remember? So what these Japanese leaders believed is completely irrelevant. Completely. The only thing that mattered was the intel we had, the beliefs we had based on years of hard fighting in the island hopping campaign to get there. That showed us the Japanese were incredibly hard fighters who did not give up. Admirable, and a bit daunting as an enemy. We had seen far too many kamikaze attacks, far too many garrisons fight literally to the last man. There was no reason to believe the Japanese would surrender, particularly when you realize they would be defending their home soil. If anything, there was good reason to expect them to fight harder, if that were possible. So yes, we hit them with weapons to demonstrate the utter futility of continuing, that we would be able to destroy them without incurring unacceptable losses ourselves.
You know, that is a very good and often overlooked point: the only hope the Japanese had of "saving face" was through some sort of negotiated settlement and the ONLY way they could get there was by dramatically increasing American deaths, so we would seek an end to the fighting.