"On June 22, the Emperor met with his ministers, saying “I desire that concrete plans to end the war, unhampered by existing policy, be speedily studied and that efforts be made to implement them.”
The attempt to negotiate a peace via the Soviet Union came to nothing.
There was always the threat that extremists would carry out a coup or foment other violence.
On July 26, 1945, the Allies issued the Potsdam Declaration demanding unconditional surrender. The Japanese government council, the Big Six, considered that option and recommended to the Emperor that it be accepted only if one to four conditions were agreed upon, including a guarantee of the Emperor’s continued position in Japanese society. The Emperor decided not to surrender."
An unconditional surrender is not a offer–it is a statement of what is going to happen. No conditions of retaining the emperor would be made.
The Japanese Junta then tried to assert conditions, which would not have been accepted, and a decision was made.
Unconditional surrender isn’t just florid language its an agreement about what you are going to do. No separate peaces. No retained kings. No amnesties or paroles. If the USA wanted to keep the emperor that would be at their fiat with no strings attached and for their own reasons.
The Kaiser was even more involved in that war and it wasn’t entirely clear that he’d be ejected and forced to abdicate either, despite his participation at the level of a field marshal/head of state/army. It was only after his support collapsed that he abdicated. Woodrow Wilson was influential in this by stating neither that he would be deposed or stay but that he would not be allowed at the negotiating table but that prosecuting him and extraditing him was not in the US interest. So the US removed his relevance by saying that any surrender would not involve him as a substantial party (ie by not recognizing him as the de jure or de facto head of state.)