I would have the game acknowledge that there are seven distinct flavors of "castable magic"; the 6 full casters, plus psion.
I would divide up the different effects of "castable magic" relatively equitably among these 7 types of magic, attempting for as little overlap as possible. (Think something like MTG, just with 7 colors instead of 5).
I would have the focus of wizard (arcane) magic be force effects, time and space effects, and metamagic effects (like dispel magic and counterspell).
so arcane, divine, primal, wild, infernal, bardic and psionic? what do you think of the following?
arcane: spells with specific 'complex' effects, 'crafted' magics.
divine: divination, buffs and abjuration, the most powerful healing and radiant damage spells.
primal: plant, animal and nature spells, summon spells for beasts/fey/elementals, light healing.
wild: simple and straightforward 'natural' magics, elemental damage, 'innate' themed spells.
infernal: spells that debuff or inflict additional conditions, or strong but awkward to use spells.
bardic: the jack of all trades, gets access to a bit of everything.
psionic: the powerful psychic and force damage spells, mental affecting spells and telekinesis