A warlord:
Base it on a martial cleric's chassi: d8 hit dice, martial weapons, all armors and shield.
Then strip away everything that fighters and clerics get on top of this, to make room for some seriously cool warlord-y abilities.
Crib freely from existing classes. The argument "the Bard already got Inspiration" is not valid - we can't have a Warlord if existing warlord-y abilities can't be used.
Extra Attack becomes Commander's strike something. You don't make an extra weapon attack, somebody else does. [Insert design discussion about how to prevent nova riders, most notably sneak damage, using easy non-convoluted language]
Possibly superiority dice, but with its own selection of support-y usages.
Full free unrestricted action trading (essentially giving up your own action to give away an action surge) at high level. Anything that requires the recipient to pay a cost in actions is dead on arrival - at high levels optimized characters have already found uses for their action, bonus action, reaction (if not more actions). Any ability that requires the target to spend its anything will get a "thanks but no thanks" response.
Absolutely no magic, or even supernatural, fluff (nothing like barbarian ancestor spirits). Pure unadulterated charisma willpower and leadership to explain 100% of abilities.
Including healing, and effective healing at that (possibly restricted to one subclass, since in-combat healing is much less a needed thing in 5E)
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Personal wishes:
At least one subclass specializing in aggro control (or "taunts" or whatever you want to call it). I know some of you will get an aneurysm just by reading this, so let's put all the aggro mechanics in the subclass (and not the base class) and then make that subclass optional.
But having a D&D class that can influence monsters to make bad decisions (such as ganging up on the impenetrable fighter while leaving the rogue and wizard alone) in a completely unmagical manner would be highly refreshing tactically and gameplay speaking.
Compare aggro to fear. It targets will (probably), but there are no attempts to write it off as something magical. A dragon's majestic aura works within an antimagic zone. Aggro should too.
Darkness and silence is another thing. I'm okay with a Warlord having a Bard-level dependency on sight and sound.