In general I like the approach of filling out new concepts with subclasses, and this is especially true for concepts that are designed to add cultural flavor to classes (as opposed to having an entire class for something like Kensei), as I feel base classes should be as setting agnostic as possible.

However, I can think of a handful of concepts that are broad/meaty enough archetypes in the realm of fantasy that they deserve to be made into base classes, and there's no reason they shouldn't be given the class roster we have including somewhat arbitrary picks like Sorcerer and Paladin already. Here are five I would make. Thankfully, there are some homebrew ones that I can use if WoTC never pulls the trigger.

Warlord/Marshal (martial strategist/non-caster)
Magus/whatever (arcane half-caster)
Witch (primal arcane/divine caster)
Shaman (spirt-based caster)
Scholar (skill/knowledge strategist/non or third caster) 

I also saw a homebrew Emergent class that I really liked and intend to use in my campaigns because it's highly unique and is a badly needed new non-caster option.

Which do you feel this way about?

• Int-based non-caster other than rogue*
• Another non-rogue Int-based non-caster*
• Mind-mage/psionicist/mystic/whatever
• Non-religious healer
• Arcane half-caster**
• Hippie***
• Unarmored divine caster****

*Artificer, strategist, scholar, knower-of-things, whatever. 

We have a divine half-caster class, a druidic half-caster class, a martial wizard subclass, multiple martial bard subclasses, a 1/3-arcane-caster fighter subclass, several barbarian subclasses that dabble in magic, a martial warlock subclass, a martial warlock Pact Boon, and probably something I'm forgetting, but we don't have any way to play an arcane half-caster without multiclassing or doing some serious reskinning. 

***Like the UA version of the Oath of Redemption, but more so. 

****Thank you for pointing this out, Einlanzer.