Hmm. Taking another tack/swing...looking at things -not necessarily as I would want them, but as they might go, given what 5e already has/does...perhaps tying things back into more abstract elements of the classes, like Primary/secondary Abilities and Alignment (perhaps even as "requirements?" GASP!) to try to fill out their stable of potential characters.
Namely, you have the "Big 4" cardinal classes: Warriors, Wizards, Mystics [nee Priests], and Rogues.
In keeping with tradition, these are the classes of: Strength, Intelligence, Wisdom, and Dexterity, respectively.
Constitution and Charisma are, and have always been (perceptions or traditions of "drop stats" notwithstanding), the "important for anybody/all characters." So they generate the rest of the "primary class" mix. Str/Con, Str/Cha, Int/Con, Int/Cha, etc...
Subclasses from there, then, incorporate the various themes and flavors common to the class with or without secondary or tertiary ability requirements, alignment restrictions, perhaps even race restrictions and other factors. Make classes that are supposed to be rare in the game world, actually DIFFICULT and rare to find/play!
OH, and what did we learn from 5e?
1. Not everyone needs spells! As I have known and used for a looong time (and do exactly as Lowkey suggests), there are "caster" classes (wizards and mystics) and there are non-caster classes (warriors and rogues).
2. Everybody should be getting a similar -if not same- number of starting subclass archetypes. Not 7 for this guy, and 2 for this one. No. Not doing that again.
Which gives us a complete 6e Players' Handbook class list looking something like...
"Basic" Game Foundation (2 Base + 6 subclasses of casters, 2 Base + 6 subclasses of non-casters)
Cleric (Wis 10): straight up cleric.
- Crusader (Wis 13/Str 10) : more weapons/armor, less spells
- Healer (Wis 13/Int 10): more spells, less weapons/armor
- Avenger (Wis or Str 15/Wis or Str 13/Dex 10): weapons, armor, spells, Roguish tricks/skills.
Fighter (Str 10): straight up fighter.
-Champion (Str 13/Dex 10) : strongman/weapon expert, access subset of fighting styles different than Battlemaster
-Battlemaster (Str 13/Int 10) : the strategic combat expert, access to subset of fighting styles different than Champion
-Hero (Str or Con 15/Str or Con 13/Cha 10) : weapon expert, strategic expert, all fighting styles, Roguish tricks/skills.
Mage (Int. 10): straight up mage["wizard"].
- Illusionist (Int 13/Dex 10) : phantasmal magic, some arcane magic, enchantments, sneaky tricks
- Necromancer (Int 13/Wis 10) : necromantic magic, some arcane magic, healing, undead summoning and control
- Witch (Int or Wis 15/Int or Wis 13/Cha 10) : phantasmal & necromantic magic, enchantments & healing, "Witch's Craft."
Thief (Dex. 10) : straight up thief["rogue"].
- Assassin (Dex 13/Str 10) : flippy flip tumble jump, stealth, sneaky tricks
- Investigator (Dex 13/Int 10) : deductive reasoning, search and perception bonuses, sneaky tricks
- Swashbuckler (Dex or Str 15/ Dex or Str 13/Cha 10) : flippy flip, search/perception bonuses, sneaky tricks, Fightery styles/skills.
Second "Advanced" tier of Classes (3 Base + 6 subclasses of non-casters, 3 Base + 9 subclasses of casters + 3 subclasses of supernatural powers without spell use)
Barbarian (Str 13/Con 10) : default barbarian. NO SPELLS!
-Berserker Barbarian (Str or Con 13/Str or Con 13/Wis 10) : more raging, less skills/tricks, more damage without raging
-Reaver Barbarian (Str or Con 13/Str or Con 13/Dex 10) : less raging, more skills/tricks, more attacks without raging
-Totem Warrior (Str or Con 15/Str or Con 13/Cha 10) : supernatural nature/"spirit" powers, magical trances.
Bard (Wis 13/Cha 10) : default bard.
-Lore Bard (Wis or Cha 13/Wis or Cha 13/Int 10) : more spells, more knowledge, less combat skills/tricks
-Skald (Wis or Cha 13/Wis or Cha 13/Str 10) : less spells, less knowledge, more combat skills/tricks
-Jester (Wis or Cha 15/Wis or Cha 13/Dex 10) : less spells, less combat ability, more skills/tricks, "Rhymes & Jokes."
Druid (Wis. 13/Con 10) : default druid.
-Land Druid (Wis or Con 13/ Wis or Con 13/Int 10) : more spells, less shapeshifting, summoning/controlling plants & the elements.
-Beast Druid (Wis or Con 13/Wis or Con 13/Str 10) : less spells, more shapeshifting, summoning/controlling animals
-Shaman (Wis or Con 15/Wis or Con 13/Cha 10) : less spells, less shapeshifting, summoning/controlling "spirits" [elemental/fae/shadow/undead], "Spirit Walking."
Knight (Str. 13/Cha 10) ; default knight. NO SPELLS!
-Questing Knight (Str or Cha 13/Str or Cha 13/Con 10) : combat/damage expertise, more individual effects, different Virtues than Cavaliers
-Cavalier[Banneret] (Str or Cha 13/Str or Cha 13/Int 10) : combat/attack expertise, more area effects, different Virtues than Questing Knights
-Paladin (Str or Cha 15/Str or Cha 13/Wis 10): supernatural divine powers, magical auras.
Ranger (Dex. 13/Con 10) : default ranger. NO SPELLS!
-Hunter Ranger (Dex or Con 13/Dex or Con 13/Int 10) : more movement, less armor/weapons, different tricks/skills than Vanguard, increased Preferred Enemies hit bonus
-Vanguard Ranger (Dex or Con 13/Dex or Con 13/Str 10) : less movement, more armor/weapons, different tricks/skills than Hunter, increased Preferred Enemies damage bonus
-Warden (Dex or Con 15/Dex or Con 13/Wis 10) : supernatural nature powers, magical trances & auras.
Warlock* (Int 13/Con 10) : default warlock.
-Tome Warlock (Int or Con 13/Int or Con 13/Wis 10) : more spells, less weapons/armor, different invocations than Blade warlocks
-Blade Warlock (Int or Con 13/Int or Con 13/Str 10) : less spells, more weapons/armor, different invocations than Tome warlocks
-Pact/Binding Warlock (Int or Con 15/Int or Con 13/Dex 10) : less spells, less weapons/armor, all invocations, summoning/controlling extradimensional minions.
Tertiary "Appendix" tier of "Power Point" Classes (3 Base + 9 subclasses all supernatural powers with or without spell use)
Monk (Dex or Con 15/Dex or Con 13/Wis 10) : default monk. Power Points: Ki.
-Sun Monk (Dex or Con 15/Dex or Con 15/Cha 10) : glowy enlightened soul, supernatural radiant magic powers kung-fu warrior.
-Shadow Monk (Dex or Con 15/Dex or Con 15/Int 10) : ninja ninja ninja, supernatural shadow magic powers ninja
-Dragon Monk (Dex or Con 15/ Dex or Con 15/Str 10) : SKA-DOOSH! supernatural nature/elemental magic powers mystic.
Psychic (Int or Cha 15/Int or Cha 13/Con 10) : default psychic. Power Points: Psy.
-Telepath (Int or Cha 15/Int or Cha 15/Wis 10) : talking to and controlling other minds
-Telekinetic/Kineticist (Int or Cha 15/Int or Cha 15/Dex 10) : moving other stuff with your mind.
-Psychic Warrior [basically a Jedi] (Int or Cha 15/Int or Cha 15/Str 10): some mind tricks, some moving stuff, psychically energizing your weapons/attacks.
Sorcerer** (Int or Wis 15/Int or Wis 13/Cha 10) : default sorcerer. Power Points: Sorcery.
-Elementalist^ (Int or Wis 15/Int or Wis 15/Con 10) : more spells (related to player choice of element), less armor/weapons, different meta-magics than Favored Souls
-Favored Soul^^ (Int of Wis 15/Int or Wis 15/Str 10) : less spells, more armor/weapons, different meta-magics than Elementalists
-Wild Magus (Int or Wis 15/Int or Wis 15/Dex 10) : less spells, all metamagics, supernatural arcane magic effects, magical mantles
* All Warlocks, contrasting to 5e, still choose a Patron as a primary 1st level thing, and while still dictating certain features, is more of a flavor thing than the importance and defining features of a Warlock's Pact. Default Warlocks are assumed to have paid/given up something (their soul, their youth, their sanity, etc...) slowly eroded/tainting them as they increase in power.
** The "origin" of Sorcerers is completely immaterial and a matter of pure character background fluff and flavor determined by the player and/or DM. And type of Sorcerer could be born with magic for any number of reasons.
^ "Elementalists" have options far beyond the 4 elements. Choose from the following options: air, animals (and/or any subset thereof: just birds, just fish, etc...), earth/stone, fire, force, light/radiance, metal/magnetism, plants/vegetation, shadow, water and/or ice, weather.
^^ "Favored Souls" are reflavored/-fluffed as a catch-all to not simply beings of Celestial connection or magic, but empowered by any being of magical origin: dragons, genies, celestials, fiends, archfey, etc... It's about the combat abilities and types of extra magical damage/effects they can do. So "Favored Souls" could be what we think of now as "Draconic Sorcerers" or "Celestial Favored Souls" or "Fae-Knights" or whatever.