The idea of using the bomb as a "demonstration" was only briefly considered. The four physicists who were asked about it concluded that they didn't think it would convince the Japanese and that only "direct military use" would likely work. You can read more here.

In retrospect, this is not extremely convincing from a due-diligence point of view: I mean, what expertise did this four physicists have on the Japanese diplomatic situation, their likely perception of the bomb, etc.? They're qualified in many things, but this isn't one of them.

But you have to remember, the goal in using the bomb was not to spare Japanese lives. The goal was not to end the war with a minimum of Japanese casualties. The goal was to make a spectacle of the first use of the atomic bomb, both in the hope that it would convince the Japanese high command to surrender, but also because the scientists hoped that the world would "wise up" about eliminating war in the future if it saw what these weapons really could do.

I think this is the point that often trips people up in retrospect: they think that the goal was to be "moral" in a very specific sense. That was not the goal of the small group of people who were in charge of these decisions. Their goal was destruction. They saw that, to be sure, as a means to an important end — but that was the means they thought the bomb was best suited for. There were those at the time who objected, and who didn't share this feeling, but they were not in control of the project, so their voices didn't go very far.