I can't speak for other time periods, but during arguably the height of the system under the Tokugawa Shogunate from roughly 1600-1860 this was really not achievable nor desirable. The Emperor was seen as the moral and spiritual center of the country as well as a kind of demi-god. According to Japanese traditions, the emperor was directly descended from the goddess who created Japan which made him pretty much inviolable. He was not simply the most prestigious or highest ranking noble, he was a holy person. Even when the Shogun militarily and politically dominated the country he still claimed to be ruling on behalf of the emperor, rather than ruling in his own right.

Of course the extent to which people truly believed this varied and the emperor was extremely marginalized politically. For the most part, however, he commanded immense respect. In fact, being perceived as acting against the Emperor's wishes was what partially contributed to the fall of the Tokugawa Shogunate in the late 1850s and early 1860s. During this time the Shogunate government signed a treaty with the United States opening the country to foreign trade without the consent of the Emperor. Additionally the Emperor was also not allowed to have a say in choosing who would become the next Shogun. These twin actions helped launch a moment to overthrow the Shogun and undermined its legitimacy throughout Japan. This is not to say that numerous other factors didn't come into play as well.

With this in mind it is easy to see why the Shogun's had no real desire to overthrow the Emperor. He gave them political legitimacy, was a religiously revered figure, and for the most part completely absent from actual political decision making.

Sources

-East Asia: A New History by Rhoads Murphy

-The Making of Modern Japan by Marius Jansen

Please see all three answers in this thread.