This. The schools are too imbalanced for such a simple approachs to work. The 5e PHB specialists sort of took this into account by giving some schools better special abilities.
My strongly held opinion is that approach used for 3.5 Psions was the right one. In a nutshell, each "specialist" had a list of "spells" that were exclusively available. Thus the specialist could gain a boost in their area of expertise, while balance between specialties is easier to attain.
Unfortunately, there seems to be a bit of an allergy in the community regarding allowing, say, Illusionists to actually be better at illusions than other wizards. It is very difficult to square that circle.