That would work nicely in an abstract spherical Japan in pure vacuum.
The hardest bit about redoing something from scratch is not how to design the new system, but it's in getting it adopted. Many societies have tried things like that, social inertia, especially paired with learning barriers (the steeper, the worse), and cultural and political notions (and Japan values and tries to preserve their history and culture quite a lot) is not something that can be just dismissed.
That's not to say that there weren't countries that had writing system overhauls, just that it's difficult and of questionable value and not entirely without negative effects.
The hardest bit about redoing something from scratch is not how to design the new system, but it's in getting it adopted. Many societies have tried things like that, social inertia, especially paired with learning barriers (the steeper, the worse), and cultural and political notions (and Japan values and tries to preserve their history and culture quite a lot) is not something that can be just dismissed.
That's not to say that there weren't countries that had writing system overhauls, just that it's difficult and of questionable value and not entirely without negative effects.