...well, the Wizard is WAY too many archetypes stuffed into one bag. It has to be every version of every spellcasting tradition from every myth and story ever--Gandalf and Merlin and Yensid and Ged and Harry Potter and, and, and, and. Make multiple Wizard-esque spellcasters that are more focused, and thus more textured and interesting.
I would say that the wizard isn't so much stuffed with archetypes so much as the label is over-used and sometimes out of context.
Much of Gandalf is based on Väinämöinen the bard. Merlin is based on Myrddin Wyllt the bard. Ursula Le Guin based much of Earthsea on Norse Mythology and Ged sang a song of ancient power when he accidentally summoned the Gebbeth. Harry Potter seems a lot less into spell books and more into strength of personality and courage, and seems more like a sorcerer to me.
I think the term "wizard" is overapplied because outside of DnD and the distinction would be something people aren't aware of. Wizards are also just bards who forgot their origins. ;-)
As it stands, the Wizard's stupidly massive emphasis on its stupidly powerful spell list means the class is essentially empty. The only class feature it gets in 5.0 between level 1 and level six-freaking-teen is Arcane Recovery. Even with 5.5e, from level 1 to 17, your actual class features (since ritual casting is just...part of being a spellcaster now) are: Arcane Recovery, expertise in one Wizard skill you've already trained, and...swapping out one prepared spell per short rest.
I don't disagree that the wizard emphasizes spells, but I think this point reaches a bit.
First Level: The wizard is very much defined by the broad spell list and also the spell book. No other class in the game uses this mechanic (unironically
Book of Shadows from the Pact of the Tome is the only similar option). Ritual casting is a feature inherent to spell casting, yes, but Ritual Adept is not. This wizard feature allows for wizards to be the only class that doesn't prepare rituals to cast them. Additionally, wizards can swap out a cantrip on a long rest where bards, clerics, druids, sorcerers, and warlocks (outside of Pact of the Tome) can only swap cantrips when they level up.
That seems like spell casting packs more in to wizards than other classes.
Additional abilities you mentioned are Arcane Recovery, Scholar, and Memorize spell. The abilities that weren't mentioned were the subclass abilities granted at levels 3, 6, 10, and 14; and the feats at levels 4, 8, 12, and 16. Those are part of the class progression too. After level 16 there's Spell Mastery, an Epic Boon, and Signature spells.
By my count it's 16 abilities in the class progression: Spellcasting, Ritual Adept, Arcane Recovery, Scholar, 4 subclass ability levels, 4 feat levels, Memorize Spell, Spell Mastery, Epic Boon, Signature Spells. Just because other classes also get some of those doesn't make them cease to exist on the wizard table. ;-)
When we compare that to the warlocks we see 14 in the class progression: Eldritch Invocations, Pact Magic, Magical Cunning, 4 subclass ability levels, 4 feat levels, Contact Patron, Mystic Arcanum, an Epic Boon, and Eldritch Master. Eldritch Master is just Magical Cunning getting better and Mystic Arcanum is just access to higher level spells like the wizard gets without calling it a class feature; neither of those should count to what we see in the class progression or we should count access to higher level spells for the wizard too. ;-)
Sorcerer (16): Spellcasting, Innate Sorcery, Font of Magic, Metamagic, 4 subclass ability levels, 4 feat levels, Sorcerous Restoration, Sorcery Incarnate, an Epic Boon, and Arcane Apotheosis.
Out of these 3 classes wizards are gaining better spell access; warlocks are gaining invocation access; and sorcerers are gaining metamagic.
Bard (17): Bardic Inspiration, Spellcasting, Expertise, Jack of all Trades, only 3 subclass ability levels, 4 feat levels, Font of Inspiration, Countercharm, Magical Secrets, Superior Inspiration, an Epic Boon, and Words of Creation.
Cleric (16): Spellcasting, Divine Order, Channel Divinity, only 3 subclass ability levels, 4 feat levels, Sear Undead, Blessed Strikes, Divine Intervention, Improved Blessed Strikes, an Epic Boon, Greater Divine Intervention. Also 16 and I don't think Sear Undead, Improved Blessed Strikes, and possibly Greater Divine Intervention should count because they're all just improvements on already existing abilities.
Druid (18): Spellcasting, Druidic, Primal Order, Wild Shape, Wild Companion, 4 subclass ability levels, 4 feat levels, Elemental Fury, Improved Elemental Fury, Beast Spells, an Epic Boon, and Archdruid. Druidic and Wild Companion are just additional spells, and Improved Elemental Fury is just Elemental Fury improvements similar to Improved Blessed Strikes.
The wizard isn't really shy of other major spellcasters in the class progression, and they all have periods where adding spell levels is the only significant increase to the class.