I think the choice between these affinities and the D&D schools would largely hinge on one of two viewpoints in deciding how magic is built fundamentally.

1) the utility and general effect of a person's magic is intrinsic, and they learn to express that form through various elements or "lenses." (D&D system) Someone born into Evocation would be able to utilize that through blasts of fire, lightning, ice, force, sound and so on, but night need training to branch out to Conjuration before they can summon anything.

2) the flavor of one's magic is intrinsic, and how they refine it to specific uses is learned (your original system and mine). Someone born of pyromancy can shoot blasts of fire and summon fire elementals, but might need training to branch out and perform those same blasts or summons for lightning, ice, force, sound and so on.

Personally, for a non-stats non-dice rp, I prefer the 2nd method.