Here's a wild eyed speculation based on no knowledge of the real people or situation.
We sometimes give to much credit for thoughtfullness. One possibility is that the "unconditional surrender" is just a habit of thought. These "bad guys" started this, we are obviously beating them, we have an ace up our sleeve so of course it is "unconditional surrender". They may simple have not thought it trough well enough.
In any case, I can't figure any justification for the Nagasaki bomb so close after the first one. It seems to me that time should have been allowed for the impact of Hiroshima to sink in.
Does anyone know what the justification for that is?