Ath'kethin
Elder Thing
It would be a long while to work it out, but I would be able to balance things like that. If I think Fireball is plenty good, I can lock its current effect for only Evocation, and everyone else gets a weaker fireball, maybe with reduced radius. Or, if I don't care about balance, I can make fireball bigger for Evocation, something like double the radius and a bigger damage die.
Wizard would still be flexible, his niche, but you wouldn't be grabbing the same exact spell list no matter your wizard school.
I was thinking of something like a specialist casting spells from their specialty as though they were a level higher than they actually are, but that would have no effect in 5e. Maybe spells count as one (or two) levels higher for non-specialists? This would delay non-spec access to spells and prevent all but specialists from casting the most powerful spells in the school.