I don't see any reason why a demonstration of our power would have worked. Demonstration of force doesn't show intent to use force, which is exactly what Japan was banking on. They had already lost, and they knew it. The US could destroy Japan with a conventional invasion, but they were hoping for favorable terms because the US didn't want to invade, because it would be so costly in terms of lives and money.

Demonstrating the bombs instead of using them simply would have reinforced the idea that if Japan held out, and waited for better terms of Surrender, they would eventually get it.

The US couldn't ever allow Japan to be a threat ever again, much like Germany. We weren't going to accept anything less than total and unconditional surrender because doing so would allow the possibility that The Empire of Japan would rise again and threaten us.

There were a lot of things that went into using the bombs. Do I agree with using them on a civilian populace instead of military targets, like a naval base or military base? Of course not. But not using them wasn't an option either. Not when the alternatives were not guaranteed to work either (using the bombs wasn't a sure thing), or an invasion that would kill millions.

The US was looking at "conservative" US casualty rates around 500,000 and millions of Japanese casualties. Other estimates out US casualties in the millions and Japanese casualties in the tens of millions, as high as 20 million. That, too, is unacceptable,but if we had used our two bombs in "demonstrations", we might have been forced to invade. The US didn't have hundreds of bombs available, we had 2. And we got lucky that it was only 2 that convinced Japan that the US was willing to completely destroy them rather than give them the terms they wanted.

I see the "demonstration" idea thrown around often, but I never see anything that supports why it could work, and I see plenty proving that it wouldn't have worked. I want to believe that there were better options than bombing two cities full of innocent civilians, but there really weren't many better options, not when the alternative was an invasion that would have killed millions, if the Battle of Okinawa was any indication.