This question gets asked quite a lot, so more answers are always welcome. In the meantime, you may enjoy these previous answers:

Why wasn't Emperor Hirohito tried for war crimes following WWII, and what reasons did General MacArthur have for steering things this way? as answered by /u/TheWinStore

Just Finished Herbert Bix's Hirohito and the Making of Modern Japan. What's the Scholarly Consensus? Is Hirohito a War Criminal? as answered by /u/kieslowskifan

After the Empire of Japan's defeat in WW2, why wasn't Emperor Hirohito put on trial for war crimes? as answered by a deleted user

Why was Emperor Hirohito allowed to keep the throne after Japan's unconditional surrender in World War 2? as answered by /u/restricteddata

Hirohito often gets lumped in with Hitler as an evil dictator in popular parlance, but to what degree can we actually lay the blame for Japanese atrocities like Nanking and Bataan on him? as answered by /u/Catfulu

It was the price for surrender. Incineration of Japanese cities, a Soviet declaration of war, blockade and US advance across the Pacific and reverses on the Asian mainland hadn't done it.

Even after the second nuclear attack and with a million Soviet troops moving into Japanese-occupied Manchuria, Tokyo on August 10 stated that:

The Japanese Government are ready to accept the terms enumerated in the joint declaration which was issued at Potsdam on July 26th, 1945, by the heads of the Governments of the United States, Great Britain, and China, and later subscribed to by the Soviet Government, with the understanding that the said declaration does not comprise any demand which prejudices the prerogatives of His Majesty as a Sovereign Ruler.

US leaders at last recognised that some concession on preservation of the throne was needed to end the war, as urged by military chiefs and on July 2 by Truman's war and navy secretaries and the then acting secretary of state, only to be omitted from the July 26 Potsdam ultimatum.

Washington's reply on August 11 demanded that:

From the moment of surrender the authority of the Emperor and the Japanese Government to rule the state shall be subject to the Supreme Commander of the Allied powers who will take such steps as he deems proper to effectuate the surrender terms. The ultimate form of government of Japan shall, in accordance with the Potsdam Declaration, be established by the freely expressed will of the Japanese people.

That was enough for Hirohito to over-rule his military hardliners and notify the Allies on August 14 that

1. His Majesty the Emperor has issued an Imperial rescript regarding Japan's acceptance of the provisions of the Potsdam declaration.
2. His Majesty the Emperor is prepared to authorize and ensure the signature by his Government and the Imperial General Headquarters of the necessary terms for carrying out the provision of the Potsdam declaration. His Majesty is also prepared to issue his commands to all the military, naval, and air authorities of Japan and all the forces under their control wherever located to cease active operations, to surrender arms and to issue such other orders as may be required by the Supreme Commander of the Allied Forces for the execution of the above- mentioned terms.

(The exchange is reproduced here.)

Hirohito's retention of the throne thus wasn't some oversight or later improvisation, it was an intrinsic part of the surrender package. In fact it was the crucial part of the surrender package, because without it there'd been no sign of Japan yielding even as its position collapsed and cities burned.

Acting secretary of state Grew had warned on June 13 that:

Every evidence, without exception, that we are able to obtain of the views of the Japanese with regard to the institution of the throne indicates that the nonmolestation of the person of the present emperor and the preservation of the institution of the throne comprise irreducible Japanese terms.... Failure on our part to clarify our intentions in this regard...will insure prolongation of the war and cost a large number of human lives.

Events were to prove him right: the bombings hadn't produced surrender, keeping the throne did. And that's why Hirohito stayed.

Wow. Thank you very much for all of this information and the sources. Very interesting!