You might want to read this recent one here , by u/ParallelPain and me, on why the shogun never tried to replace the emperor. The most relevant information to the question should be somewhere in there.

Also, if you got too much free time you can also check out the respective section in the FAQ in addition, for more circumstantial information: https://www.reddit.com/r/AskHistorians/wiki/asia#wiki_japan , section on The Emperor and the Shogun. I also have an earlier answer somewhere on the whole idea of rule by the abdicated emperor, if that's still not enough.

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But the very short tl;dr:

Why replace the emperor, other people governed in his stead most of the time anyway. (also, we can't say for sure why it never happened because it never happened)

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If there's open questions after this, feel free to ask.

The scholarship linked to here is reasoned and well-sourced, so not looking to impugn that.

But I think in all honesty this is one of those questions that doesn't have a truly compelling answer other than "they didn't replace the imperial line because they didn't."

Any appeal to custom or tradition you can make can find countless counter-examples. Divine sovereigns are quite common in premodern history, and all you need to replace one is to create a narrative afterward that they'd done wrong and lost the favour of the gods. There were plenty of analogues in Chinese history that would have served as valid precedent. Heck, both Hideyoshi & the Tokugawa themselves tried to play the divinity card in their own fashion.

The "it would have caused political turmoil" argument contradicts the notion that they persisted through their own powerlessness. There were many inflection points throughout history when the imperial house had comparatively little access to material resource, and the decline of the aristocracy paralleled this. The risk would have been that an ambitious regional samurai leader would have seen an opportunity and used the excuse of taking up the emperor's flag to rebel, but there were certainly times when there wasn't a sufficient threat present.

I think rather than tripping over teleologies in looking for Big Answers, the way to view it is probably as a long series of idiosyncratic decisions which were made for their own reasons in their own time, which ultimately added up to a historical rarity.

Others (such as u/Morricane ) have already touched on varying conditions which might have led to the endurance of the Japanese Imperial Family. I will attempt to explore another layer of this, that being the concepts of ideological legitimacy which provided the foundation for the Imperial Family's place in Japan. By this I am referring to the relationship between the Imperial Family and the divine. u/S_Belmont has already brought up a counter argument to this, when discussing how concepts of “divine sovereigns” or common throughout history, such as with China. But the concepts themselves (between Japan and other cases, such as China) are different, and it’s in this distinction that we find a possible reason (again, one of many) as to why the Japanese Imperial line was able to endure where others may not. To mark this difference, I will compare the concept surrounding the Japanese Imperial line, and China (as you brought it up specifically).

I will first speak on the Chinese concept of ideological legitimacy we see, that being the “Mandate of Heaven”. I will refrain from going into too much detail, as Chinese history is not my area of focus per se, and welcome any of the resident Chinese history flairs to add on more context/nuance if necessary. The basic explanation of the “Mandate of Heaven” (tianming) is that the Heavens bestowed, upon Emperors, divine authority to rule on earth, on behalf of the divine. There are two aspects of this to note, as it pertains to the comparison we are exploring. One, is that no single family, or dynasty, had a monopoly on the Mandate in perpetuity. If a ruler did not conduct themselves properly, the Heaven’s could bestow the Mandate on an unrelated person. Tied to this is point two, being that the “Mandate of Heaven” had a performative quality. Real world conditions (such as floods, famines, etc) could be viewed as the Heavens providing indication as to their view of the state of the Emperors place in accordance to the Mandate. In the article ‘The Mandate of Heaven and Performance Legitimation in Historical and Contemporary China’, Dingxin Zhao describes this aspects when saying:

“The strong performance aspect of state legitimacy allowed the ancient Chinese people to judge their ruler in performance terms. In historical China, the people viewed natural disasters and famines, therefore, as signs of unfit rule and perhaps even a coming dynastic change. This kind of mentality inspired thousands of peasant rebellions throughout Chinese history. Although most rebellions were ruthlessly repressed, the idea of rising to rebel against an unfit ruler had a legitimate position in Chinese political culture. That was why Chinese were always ready to accept a rebel leader as the new ruler as long as he was able to stage a successful uprising. This way of thinking was so pervasive that even the successful nomadic invaders justified their conquest of China by claiming that the rulers of the overthrown Chinese dynasty had lost the mandate to rule because of their poor performance. The Chinese proverb “winners are kings and losers bandits” says it all.” - American Behavioral Scientist, Vol 53, No. 3, page 422.

As this quote shows, the natural world almost served as a performance stage in which the state of the Emperor’s place, according to the Heavens, could be gauged. In certain conditions, rebellions could conceptually be legitimized as being a transfer of the Mandate. A final thing that is worth noting, is that not only could the Mandate pass from one dynasty, to an unrelated one, but that the Mandate was not restricted to some courtly elite, or to the Han-Chinese themselves.(continued in next comment)