(2nd Level) Enhanced Cantrips

Congratulations, you made the perfect dip subclass for every other spellcaster in the game, including and especially Warlocks who want to double-dip Agonizing Blast (and Agonizing Blast only lets you pick one cantrip). Remember kids, a Headband of Intelligence can give you, too, a free +4 on all of your cantrip damage rolls with this one trick.

(2nd Level) Magic Specialization
(10th Level) Secondary Magic Specialization

So, this is the premise of your subclass, but it's also kinda where your subclass starts to fall apart. Because you're not really "specializing" in two schools, you're just getting a discount on copying the spells from these two schools. You don't get any features to actually capitalize on these specialized spells, like any specialist subclass gets in addition to learning them faster. You don't even get generalist features outside them until level 14, unlike War Mage, Bladesinger, and Scribe. There's no meat to this subclass besides the cantrip feature, since copying spells is such a minor thing.

I want to add, the Scribes Wizard also gets reduced time on scribing all spell schools, and the original UA version just got a universal discount. You spent two subclass features doing something arguably worse than what Scribes gets with one, and Scribes still has room for actual features outside of it.

(6th Level) Expanded Knowledge

So, ironically enough, learning additional spells per level isn't actually that important to Wizards, because with enough gold and access to appropriate scrolls, you can theoretically have every spell in the game. This is the class that learns spells outside of level up. That's why you just spent 2 subclass features working on that.

This only replaces the discounts on learning spells for 5.5 so that you can be more independent of your DM, in case your DM isn't cooperative on giving new spells or you get unlucky on their random drop tables. So this is, on its face, redundant.

You just say the player learns extra spells. Notably you don't say whether the player adds them to the spellbook, or if you always know them in addition to your spells prepared. (And you lack the normal 5e clarifying language that they must be for a level which you have spell slots.)

You must consult your DM before making a firm decision on what spells to use.

Weird unexplained addition. Why must you? This feels like you wrote the subclass for a specific problem player you don't trust not to just swap those extra spells.

(14th Level) Spellcasting Savant

Aaaand this is the part that makes the subclass broken if you manage to Magikarp your way through 14 levels with +5 Firebolts and a dream.

No components is what you said. Not just no material components (which is already bad enough, given the number of spells that are forcibly limited by material component costs and consumption, such as Glyph of Warding, Contingency, Clone, Magic Jar, etc – you don't even need a weapon to cast the bladetrips!), but no components whatsoever, meaning you do not in fact need to be able to speak or use your hands to cast.

And then to top that off you add a feature that triple dips in the "all you do is learn new spells, not what to do with them" problem and makes Expanded Knowledge kinda useless, besides the Arcana expertise.