Chaosmancer
Legend
That's mostly due to the fact that wizard subclasses don't change the base class that much, while Barbarian subclasses pretty much define who you are and what you're going to do. Bear Totem Barbarians are gonna tank, Beast Barbarians are going to destroy every enemy with a flurry of primal blows, Battlerager Barbarians don spiked armor and throw themselves into their enemies. However, most wizard subclasses play pretty much the same way (other than Bladesingers and probably Necromancers).
Here are some possible combinations of two schools of magic that can be interesting, while still fitting in with the other subclasses:
Lifedrinking Magic - Combine Evocation and Necromancy to drain the life of your enemies to heal yourself and allies. They're often used in wars to work as a healer and battlemage.
Figmentation Magic - Combine Conjuration and Illusion magic to create illusions that are partially real, and can be interacted with.
Phantom Magic - A combination of Necromancy and Illusion magic to use phantasmal force, phantasmal killer, and other illusion spells that frighten people and make them see things that aren't there.
They're not all that exciting, but they still would be valid and cool subclasses.
They are cool concepts... But the illusionist and conjurer already do stuff like Figmentation magic, and Phantom magic just seems to describe a spell selection.
I know you would add abilities to them, but Phantom magic in particular seems like it is really about buffing specific spells, instead of creating a new way to play the wizard.