From what I read (although I don't remember WHERE, so take it with a grain of salt) is that we WERE supposed to get Amaterasu as a Primal in the 4.x series, but her design was too similar to Lakshmi and she ended up scrapped. I'd have loved to see her to round out the 3 siblings.

Also, Amaterasu HAS appeared in the series, or rather, some of the lesser known spin-offs. She debutted in FF Explorers and showed up as a summon in Bravely Second (which is an FF in everything but name). Susano-o also showed up in Bravely Default, although I don't remember if Tsukiyomi showed up in those, too...