The Japanese emperor has claim to a divine connection/lineage in a way that doesn't exist for the Chinese Emperors. The Japanese emperor is thought to be directly descended from the sun goddess Amaterasu through a single coupling that was thought to have taken place at a certain moment in history. While the Chinese emperors were known as "Sons of Heaven" and had religious functions/ semi-divine connotations as a representative of heaven and of the Chinese people they were not divine in the same sense as having a lineage tied back to a divine figure. While the philosophy of the Mandate of Heaven in China allowed for the overthrow of emperors and founding of new dynasties when the previous had been corrupt, a shogun could not overthrow the Japanese emperor and lay claim to his divine lineage. Having a puppet emperor with those divine claims could still be a useful political and symbolic asset to shoguns so there wasn't really a need to do away with them.

I've talked about it to some extent here.

Essentially, cultural and religious values meant that there was little gain to be had from overthrowing the Emperor, and thus there was little reason to sacrifice their position for a negligible gain of power.

It does not mean no. Shogun Yoshimitsu Ashikaga(足利義満) was trying to become the emperor, but he died just before.
But technicaly he became an emperor.
After he died, came the order to appoint him to the "Cloistered Emperor(法皇)" from the Choutei court(朝廷). After shogunate thought, gave back the order next day. In other words, only the one day Yoshimitsu was in the Emperor's place.

As a follow up question, how widely known would it have been among the population in general that the emperor wasn't actually the one calling the shots?

Follow up question, why did the Japanese Emperor not ha e as much power than the various warlords in Japan?

When this question can't understand His Majesty the Emperor's(Ten-nou) Japanese placing, I don't find a solution. His Majesty the Emperor is located in the dimension different from an emperor.

His Majesty the Emperor is a Japanese parent. The people will be His Majesty the Emperor's child (Great treasure) completely.

A Shogun (General) and a farmer become equal as His Majesty the Emperor's child (Great treasure) in Japan. All Japanese became equal with the dimension of His Majesty the Emperor as treasure from 2676 years before in Japan. So the slave who can possess doesn't exist in Japan. Everyone is a brother and all Japanese will be equal status by the dimension of His Majesty the Emperor.

Oda Nobunaga made the black people its vassal. He was the black slave a Portuguese missionary has taken from Madagascar. Nobunaga named him YASUKE and permitted a marriage. Yasuke was excellent, so Nobunaga gave him a castle and made a daimyo promote. Hideyoshi banished a Christian missionary from Japan. It's a reason that Hideyoshi has known missionaries to have dealt in Japanese men and women as a slave.

Shogun's business is to govern His Majesty the Emperor's people (Great treasure) importantly. The important treasure by which the people are His Majesty the Emperor all. So it shouldn't be injured excessively A violent person and the person who doesn't have the ability to govern can't be a shogun. Only a person with the force and the government ability was appointed as a shogun from His Majesty the Emperor consequently.

Victory or defeat of warlike ages and a war, it itself proved the government ability. A farmer changed to a soldier, and fought. In purpose of the warrior who respects them. The Shogun who isn't yearned for by the people was beat by a different warrior. A war isn't a genocide in Japan. It's a tug-of-war in Japan. In case of loss, one general (sometimes, the family) shoulders responsibility. It's hara-kiri. Death of one general secures the life of the vassal and the population of the fief.

Japan was the country it's more difficult for a dictator to exist where than ancient times. The dictator who tries to own His Majesty the Emperor's people (Great treasure) privately has been destroyed certainly. European ruler and Oda Nobunaga had a part where thought is similar. He was killed by a staff. He was a hero. But the people weren't his possession.

Present Japan also makes the same form basic. Election is a war and the political party which got national backing has the right to choose a prime minister. The person who got support most in the election in the political party will be prime minister's qualification holder. It's His Majesty the Emperor to see a result and appoint a prime minister actually.