The Bard, Warlock, Ranger, and Paladin, are designed with a strong correlation a specific combination of Spell Schools and having exclusive spells or unique effects on spells within their power source.
Yeah, as I said, classes strongly correlate with a specific combination of Spell Schools. That also applies to the Wizard, see further on.
The Spells are a separate design space, and must be, because the high tier game engine depends on how spell slots scale in power in ways that are balanced for that level, reliable and well understood.
I oppose "exclusive spells" because they are almost always overpowered (for Wizard) or underpowered (for Druid) and skew the balance of the every spell that exists in a same spell slot.
I am ok with classes "having unique effects on spells" − like Warlock modifying
Eldritch Blast and Ranger modifying
Hunters Mark − because these power boosts are part of the class design space, not the spell design space. So the Evoker Wizard can have a feature that boosts the
Fireball spell.
The Cleric, Druid, and Wizard, are designed in the image of having access to ALL Schools in their power source.
In 1e, the one class Wizard ("Magic-User") was any kind of spell casting concept, including "warlock", "sorcerer", "enchanter", "necromancer", and so on. Meanwhile, only the Wizard was a "full caster" with slots upto 9th. The other casters were part casters that could only reach the 7th slot or less. But today, there are different kinds of full caster classes. The Wizard needs to split away some schools, so it can specialize more, and so other full caster classes can have more design space for their own flavor concepts.
The Wizard is especially is known for "
Fireball", in other words the Evocation school. I also associate the Wizard with the old school Illusionist. Meanwhile, magical energy and spell research generally is part of the class concept, whence an updated sense of Conjuration that relates to the magical energy of
Dispel Magic and force constructs, as well as force
Magic Missile, telekinetic
Fly, and so on.
Enchantment makes less sense for the Wizard today, and makes much more sense for the Bard and the Warlock today.
Transmutation in the sense of lifeforms, healing, shapeshifting, animals and plants, makes less sense for the Wizard, and more sense for the Druid and Bard.
Personally, I prefer the Wizard lacks the Necromancy school, and the Cleric and Warlock focus on it. (Traditionally the Cleric is the turner or the controller of Undead and Fiend, but today also the Warlock traffics with Undead, along with Fiend and Aberration.)
And so on. Today the "full casters" do well to focus the flavor thematically, to distinguish from each other.
In the editions where base casting classes had the same power source, they shared access to some schools but had access to different sets of spells in those schools.
If the Schools are saliently thematic, they organize the spells better in the first place.
There is no need for a class to have a sloppy mishmash of any and every school. When each School is meaningful and mutually exclusive, it is clear which School is appropriate or not.
When Evocation is every elemental spell, then the Bard shouldnt have it. If Transmutation is the healing and lifeform spells, then the Wizard shouldnt have it.
Note, subclasses can modify the base class. For example, perhaps a certain Bard subclass grants access to Air Evocation spells, for wind of breath and thunder of voice − and maybe raging "flaring nostrils" and storm magic generally be part of this subclass too. But the Bard base class should avoid Evocation spells entirely.
Classes known for Evocation, in the sense of elemental magic, are Wizard, Druid, and Sorcerer.
And so on, with other schools strongly correlating with certain full caster classes.
Each full caster class leans into certain themes, and each School can update to supply the salient theme.
Compare Wizard and Psion.
The Psion feels primarily mind magic, namely the Enchantment School. From the perspective of the mind, the Psion also accesses the spells of certain other Schools including Conjuration (telekinesis and a personal magic aura separate from the ambient weave), Divination (for psychic readings and spacetime effects), and Transmutation (psychometabolism including shapechange and healing). There can be four subclasses, each to focus on one of these four schools.
By contrast, the Wizard feels primarily about Conjuration, researching the nature of ambient magic and its mysterious forces. From the perspective of the magic, the Wizard also accesses the spells of certain other Schools, including Evocation to reshape the matter of existence, and Illusion to alter the fabric reality. The Wizard is a "Creator" archetype.