I suspect, in the end, a lot is game balance as said above.
Presence as the force of ego driving mentalism makes some sense.
Intuition and Empathy for the other two realms seem vague.
The best argument for Intuition seems to be that it contains to concept of inspiration, which kind of fits the divine-to-mortal logic.
The best argument for Empathy is that it's the "feel for others" stat, including your feel for the world. . .so your Essence user is reaching out to the world to draw power, it uses empathy. It's akin to attunement, but in reverse, rather than matching your aura to an object in order to use it, it's matching your aura to the environment in order to tap into it.
I suspect it relates most to how they draw power, as opposed to how they cast. . .
Mentalist uses their force of will (Presence) to draw power.
Channeler is being inspired/opened (Intuition) to power.
Essence is pulling power from their environment via their aura using a form of attunement (empathy)
Something like reasoning based magic would likely work better if the power draw was unrelated to the caster. . .like if say you had a gameworld where magic power was available in easily used crystals. . .so you could then be a technical, reasoning caster without needing presence, empathy or intuition to draw power. . .magic as reason/logic/technology.
