you'd probably have to look into how relevant kojiki and nihon-shoki are among the modern population. both trace legitimacy of the emperor (gender biased) from the succession of heirs from the gods, and japan's own version of the imperial court did historically unify the archipelago before it became "the japan" that it is (although to what extent, versus military control, is debatable).
i don't think that gender is necessarily important--i'm sure there are females that could competently manage any nation's issues just as well as, if not better than, a male counterpart. but it's my opinion that the identity of japan is to an extent dependant on the legitimacy traced through kojiki, and while japan can be quite a progressive society (at least following WW2), i don't see modifications to the seat of the emperor being made any time soon.