Internal documents (unavailable to the Allies) show they were actually coming up with terms of surrender. But that's not fair; the Allies didn't know. Its hindsight.
The Allies responsible for making the decision did have access to intelligence reports making it clear that senior representatives of the Japanese were trying to mediate an end to the war, including explicitly quoting many of the Japanese comments - both intentional communications and intercepts - to that effect.
There's no shortage of notes to suggest that White House decision makers were aware of these and debated the possibility that including a guarantee of the Emperor's position in the Potsdam Declaration might have made surrender possible, but didn't want Russians as mediators and were more concerned about domestic opinion of demanding anything other than unconditional surrender than actually hastening the surrender. Ultimately these considerations (and others) took precedence over saving lives, and if anything is hindsight bias it's the [plausible] argument that a more stable, peaceful and prosperous Japan was achieved through insisting on total defeat and not involving any Soviet "mediation".
Well, by then we were starting to get a good take on what the post-war Soviets were going to be like, and with FDR's death and Truman, not previously an insider, the government wasn't quite so in thrall to them.
However we did signal flexibility to the Japanese about the Emperor's position; we weren't stupid, we knew that might be part of an acceptable and otherwise "unconditional" surrender.
A declaration was made and unconditional surrender requested. The Japanese were warned that they would face complete destruction if they refused. The Japanese refused. It is only at that point that the US dropped the two atomic bombs.
Indeed, and my awkward essay https://news.ycombinator.com/edit?id=10132884 shows that we know we let the Japanese know prior to the bombings the one condition we were willing to allow, maintaining the position of the Emperor (well, eventually his position was diminished, but not abolished).
The Government, that is, the ministers including Army and Navy forming their parliamentary Cabinet (NOT a US style Cabinet), rejected it out of hand prior to bombings and the Soviet invasion of the Army's precious Manchuria.
There's no shortage of notes to suggest that White House decision makers were aware of these and debated the possibility that including a guarantee of the Emperor's position in the Potsdam Declaration might have made surrender possible, but didn't want Russians as mediators and were more concerned about domestic opinion of demanding anything other than unconditional surrender than actually hastening the surrender. Ultimately these considerations (and others) took precedence over saving lives, and if anything is hindsight bias it's the [plausible] argument that a more stable, peaceful and prosperous Japan was achieved through insisting on total defeat and not involving any Soviet "mediation".