Not sure about Monk...that class is always a little weird. Probably because its like trying to fit Kwai Chang Caine from Kung Fu into Ring of the Nei....Niebelunginigninegingen...gen Lord of the Rings.
It was more of the same, really. It's a class that fights really well, but because it's not wearing armor, it couldn't be a fighter, and had to get all weird. That's been long since fixed, but it doesn't seem to matter.
One hoary concept in D&D goes all the way back, and that's the conviction that being able to wear any armor, strap on any shield, and use any weapon is a HUGE advantage.
Think about the first 4 classes:
Magic-User: Armor? NONE Shield? NONE Weapons? Dagger/Staff Magic? All of it.
Cleric: Armor: Plate Mail! Shield: Yes! Weapons: Maces &c Magic? No fun stuff, just Band-Aids for you, but oh, here, turn some undead.
Fighter: Armor: Plate Mail! Shield: Yes! Weapons: All the Best, including the most-found-magic-weapon of them all the Longsword! Whoopee! Made of awesome!
Over time, the armor you wore became little more than cosmetic, everyone could maintain a decent to good AC with minimal effort, the fighter/cleric 'dependence' on heavy armor increasingly became a disadvantage.
Shields were never worth much by themselves, but magic shields used to add a lot to your AC. That's gone.
And the all-awesome, all-the-best-magical-versions Longsword? By 3.0 just about any weapon enchantment could go on just about any weapon.
The old armor/weapon/hps balancing magic & special abilities equation has been wrecked for a long time.
However! Yes. I forgot about Barbarian and Rogue. I might argue "Rogue" because of the Assassin and Acrobat types would seem to need a home that might be an odd fit in Fighter. The thief-y stuff should probably be just a matter of skill package, IMO.
In 5e, the fighter finally made the transition to being either DEX or STR 'based' relatively seamlessly. An acrobat or assassin or monk fighter in light/no armor would be pretty painless to design.
Or a wonderfully improved Champion!

hunh? hunh? amirite?
Sure, that'd happen.
I thought they missed the design mark a little, as well with 5e (even though I think its one of the better editions by a long stretch). I feel like they had the great idea about three pillars and then just about ignored it entirely. Within the context of D&D, it doesn't make sense to try to balance out the classes looking at the pillars as a whole so that Class A being the best at pillar 1 means that they are necessarily one of the worst at pillars 2 and/or 3. Instead, we should have seen more distinction, like how Backgrounds only affect Interaction (for the most part).
Nod.
Backgrounds don't only affect interaction, and class affects interaction a lot, but the idea is sound.
Class: Combat (OK, 'primarily combat')
Background: Social/Interaction (because where you come from matters to people)
Exploration?
I'm thinking lift a term from 2e: Kit.
Backgrounds and Classes could be drawn from what's already out there, just re-focused.
Kits would have to strongly point at the exploration-pillar, including the few sub-classes/whatever that already seem focused there, Thief & Scout plus, IDK, a Sage who /knows/ all about various environments even if he hasn't visited them before?
If I were to wave my magic wand... Background would stay pretty much as is, purely answering the question "Where did your character come from?" Class (and subclass, were it kept) would answer the question "How does your character contribute to a fight?" And some sort of skill-package feature...lets call it "Specialty" might answer the question "How does your character contribute in Exploration and/or Interaction?" Specialty is where "Thief" would live, but alongside "Scout", "Diplomat" and a few others. So to get a Traditional Ranger, you would need to pick "Fighter/Ranger" and "Scout".
jeez I can ramble.
Nod. That's not overthinking the Warlord, that's overthinking everything.
It's not, particularly. Mostly I'm a just bit over people arguing that this or that character concept "deserves" to be a class
It sounds like you don't want to add classes, because you'd rather overhaul the entire class system.