I'd go with both.Tough to say.
Take Fire Elementals, as a simple example. If you divide up the spell pie such that there is a Summoner class and an Elemental class, who can summon a fire elemental? One or the other? Both? Maybe require a feat, or some multiclassing/hybrid classing?
There's not really a right answer, to me. I'm fine with a system that makes Summoner a dedicated class, or that makes it a mechanical role divided among various sources/schools, or that limits Summons to rituals and controlled with narrative hooks.
In my ideal version of summoning, it would be a school of spells, i.e. Transmutation, Abjuration, Summoning.
BUT! Balancing that concept (anyone could learn to summon, some specialize) is mad cra-za-zy difficult.