I think there's nuance here that gets lost in the retelling. From what I learned of it in a university course dedicated to many aspects of the topic of that bomb, there was a demand of /unconditional/ surrender but Japan wanted to keep their emperor. The emperor was really more of a cultural and spiritual persona than a political one, but regardless the US gov't. insisted on an unconditional surrender, including dethroning the emperor. I think there was an offer of surrender by the Japanese if they could keep their emperor. I don't have proof handy and I'm not inclined to dive down that particular rabbit hole right now so I hope someone can support or correct this.
I vaguely recall hearing something similar, with the reasoning being that there was a fear of future hostility enabled by Emperor driven fanaticism. That said, I've also heard that there wasn't really enough time given for a response after the first bomb, and that it was largely a political move to claim they'd offered an initial surrender - and that the goal was always to drop two bombs, partly because they wanted to test out different aspects of their designs.
