I'm not sure where you're getting the idea that Japan was allowed to surrender conditionally. They weren't. They accepted unconditional surrender... as for why much of the Japanese government was bureacratic mechanisms (and the Emperor) were allowed to remain in place... here's a bit from an earlier post I've made on the topic from this thread:

In short, America needed a Japan that was rebuilt and a friendly state as quickly as possible in the immediate aftermath of the Second World War. This was in order to have a stable, undivided platform from which to counter what many high-ranking military experts understood was going to be the Third World War right on the Second’s heels: the looming confrontation between the Soviet Union and the Western Powers.

As per the Yalta and Potsdam Conferences, though Japan had studiously (and much to Hitler’s dismay and ultimate downfall) refrained from declaring war on the USSR, Stalin had agreed with Churchill and Roosevelt to declare war on the Japanese Empire and invade, first their colonies in Manchuria and Korea, and then the home islands. What that meant in terms of the Western postwar outlook would be much the same as what was already shaping up in Europe: the division of such states into Soviet and Western blocs. Such a state of affairs was wholly undesirable to the US, who looking beyond 1945 saw the policy on containment of Soviet influence to be its top priority.

As late as August 10th, 1945 – after the atomic bombing of Hiroshima but before the destruction of Nagasaki – the Japanese government was still sending its request to conditionally surrender to the Allies, with their one and only condition: “that the stipulations of [the Potsdam Declaration] do not include any demand for alteration of the authority of the Emperor to rule the state.” Such a precondition were deemed unacceptable by both the US and the USSR, with Commissar of Foreign Affairs Molotov being described as “skeptical,” and thus the war carried on until September 2nd when unconditional surrender was at last accepted.

There were trials, and members of the Japanese military and civilian government were tried and between the IMTFE and the prosecutions conducted by independent nations, according to Dower some 5,700 people were convicted of Class A, B, and/or C war crimes, resulting in almost 1,000 death sentences, nearly 500 life sentences, and more than 2,900 lesser sentences. Yet some of the worst criminals, it is true, did essentially get away scot-free, most notably the commanders of the infamous Unit 731, which had been given immunity from prosecution for their human experimentation and biological weapons research in exchange for that research, and at least as important, denying the Soviets access to that research (which would prove at least partially futile).

Crucially, though [...], the Japanese monarchy and government was left largely institutionally intact. Unlike West Germany, there was no corollary to “de-Nazification” in Japan. Yes, there were purges of the extreme ultranationalists and right-wingers, but they were often allowed back ‘into the fold’ rather quickly. Why? Because especially after the shocking fall of the Republic of China to the Maoists in 1949, it seemed to most that Asia was on the cusp of toppling like dominos to communist influence. The US determined at a fundamental policy level that a stable, united, friendly, and anti-Communist Japan was absolute priority. That meant people with a proven track record of industrial, business, and managerial success – lo and behold: it was often the very same rightists.

The Emperor was declared by MacArthur and Co. to be not responsible for what had happened over the course of the war, with the blame instead falling squarely on the military brass like Tojo. Symbolically, this was significant because it allowed the people as a whole to say, in essence, that the militarists had taken over and done bad stuff, but that was them, not us, and they were already held responsible

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Dower, John. (1999) Embracing Defeat: Japan in the Wake of World War II.

Translation of intercepted Japanese messages, circa 10 August 10, 1945, Top Secret Ultra

Memorandum of Conversation, "Japanese Surrender Negotiations," August 10, 1945, Top Secret

Great, thank you for asking this question. I had a similar question today, but as it touches the third item on your list ('The Japanese respond to the Potsdam Declaration with something about "kill it with silence," and so the Allies take that as a no.' - OP), I'll post my question as a follow-up.

I'm reading 'The Making of the Atomic Bomb' by Richard Rhodes. In that book, the author says that the word used by the Prime Minister Suzuki to respond to the broadcast of the Potsdam Declaration was 'mokusatsu', and that the historians are still debating what Suzuki meant by it. The book was first published in 1986. Did we find out what Japan meant to communicate, exactly, since that time? Is is 'kill it with silence', 'ignore it entirely', or 'treat it with silent contempt'?

For the reference, here's the relevant quote from the book.

The text of that somber document [the Potsdam Declaration - sp314...] went out by radio to the Japanese from San Francisco; Japanese monitors picked it up at 0700 hours Tokyo time July 27. The Japanese leaders debated its mysteries all day. A quick Foreign Office analysis noted for the ministers that the Soviet Union had preserved its neutrality by not sponsoring the declaration, that it specified what the Allies meant by unconditional surrender and that the term itself had been applied specifically only to the nation’s armed forces. Foreign Minister Togo disliked the demand for occupation and the stripping away of Japan’s foreign possessions; he recommended waiting for a Soviet response to Ambassador Sato’s representations before responding.

The Prime Minister, Baron Kantaro Suzuki, came during the day to the same position. The military leaders disagreed. They recommended immediate rejection. Anything less, they argued, might impair morale.

The next day Japanese newspapers published a censored version of the Potsdam text, leaving out in particular the provision allowing disarmed military forces to return peacefully to their homes and the assurance that the Japanese would not be enslaved or destroyed. In the afternoon Suzuki held a press conference. “I believe the Joint Proclamation by the three countries,” he told reporters, “is nothing but a rehash of the Cairo Declaration. As for the Government, it does not find any important value in it, and there is no other recourse but to ignore it entirely and fight for the successful conclusion of the war.” In Japanese Suzuki said there was no other recourse but to mokusatsu the declaration, which could also mean “treat it with silent contempt.” Historians have debated for years which meaning Suzuki had in mind, but there can hardly be any doubt about the rest of his statement: Japan intended to fight on.

Rhodes, Richard. The Making of the Atomic Bomb. Simon & Schuster.