This is largely a response to Yoshida's commentary here.

Occasionally scavenged from the broken husks of Allegan arms and armor, Schema are Materia-like crystals bearing powerful magickal formulae designed to restructure and enhance the base form of the weapon or armor it is placed within.

[Primary Purpose]
Schema infused gear would replace Allegan gear as the “top” gear and future Allegan gear are dropped to item Level 70. Currently existing Allegan gear are modified to include the associated Schema and retain their previous item Level. AF2 equipment would maintain its current item Level 90 spot but would receive noticeably smaller returns from using a Schema (as it is already item Level 90, caps would not increase if lower or equal effective item Level Schema were used - further, Materia slots are not present on AF2 gear).