IIRC the damage inflicted by the atomic bombings weren't especially noteworthy compared to the rest of the bombing campaign, and it was more a way to test out their new toys. If the nukes hadn't been used but conventional bombing had continued, it would likely have had a similar result. This video by Shaun lays out a pretty compelling case that the Japanese surrender was due to the Soviet declaration of war and invasion of Manchuria.

This is all ignoring of course that despite the insistence of unconditional surrender, the Americans accepted surrender with conditions and allowed the emperor to continue to hold his titles anyway. There's definitely something to be said about taking maximalist positions just to make a point even when they don't actually care about several of the goals that make up those positions.