As PP already noted, the shogun was not the most powerful title in Japan, it simply came to be over the course of time that the means the imperial court had at its disposal declined. Suffice it to say, the Tenno never was an absolute autocrat who could just do whatever he wanted, despite the monarchy in theory being an autocratic government form, but always had to act within a web of interests and power balances between himself and the remaining court elites. Furthermore, Japanese society was quite subdivided between multiple authorities (such as noble houses, shrines, temples etc.), who each possessed a certain degree of autonomy by the mid- to late-Heian period (~10th, 11th century).

To simplify, in the courtly worldview, the position of shogun, as it was redefined during the Kamakura period due to its association with the ruler in Kamakura (the Kamakura-dono), designated the (warrior) leader who was acknowledged as representant of the court in military and police affairs and who had the means at his disposal to actually fulfill these functions; that he came to represent the court in matters of diplomacy etc. as well, was not exactly an intended effect, but a result of social and political developments over the course of centuries.

Either way, it follows that the notion of the Tenno giving himself a title which designates the authority to represent the Tenno logically doesn't work: we'd end up with a self-referential paradox. What, however, could happen—and, incidentally, did happen—is that the necessity of the arrangement itself disappeared: one effect of the Meiji Restoration of 1868, which simply got rid of the shogun altogether.

Incidentally, what, of course, also was possible, was giving the title to a member of the imperial family who was not the Tenno. This happened both with the later Kamakura shoguns, but also during the campaigns against the Kamakura shogunate in 1333 for very different reasons: in the former case as part of an arrangement between court and shogunate, in the latter as a means to legitimate Godaigo's military authority and at the same time, to keep this kind of warrior legitimization out of the hands of his ally Ashikaga Takauji—much to the chagrin of Takauji, who eventually produced his own "counter-Tenno" and forced Godaigo into exile.

Sei-i Taishōgun, as a title, is not more powerful than the emperor. It just de-facto became that way from history. Minamoto no Yoritomo basically took the title to justify his campaign against the Ōshū Fujiwara, and didn't really care about the title and might have gone so far as to give it up. You can see here for a (slightly dated) thread about the changing position of Shōgun.