If I look at boardgames and wargames as a starting point there are basically two functions leaders have - improving morale (including rallying broken troops) and mitigating command and control limitations. I think if you want a strong leader archetype a game needs to feature all those problems that happen in battle in the absence of good leadership.
The RPG premise of being in full control of your character runs contrary to what happens in battle. Real people fighting in melee break and run long before they get to 0 HP. They don't 'decide' to run. They run. Real people are overwhelmed by the carnage and mayhem around them in the absence of organisation and leadership. Real people look around for the reassuring presence of allies while taking offensive action. RPGs generally do a very poor job of modelling the psychology of the battlefield.
Its a fine point you make here. Typifying this is the story of Norman "Dutch" Cota rallying the pinned-down, shell-shocked troops of Omaha Beach of the D-Day invasion; "HP as morale" and "Psychic Damage as HP attrition" and "Inspired resolve to push on and fight despite your mental and physical (most of the men he inspired to take the beach were wounded with shrapnel, or worse)". A moral track would certainly facilitate that recovery well but I find that the abstract HP system can handle stress damage well enough (as well as it handles anything else with all of its unwieldiness!). A separation of stress/emotional damage would serve but D&D doesn't have that system like MHRP or Fate.
There is a reason that words such as "Rangers lead the way!" are memorialized and become the motto of the Rangers. Its because the valiant example and the sincere words of a battle captain, such as Norman "Dutch" Cota (who was definitely not a great warrior himself, eg not a Fighter), can inspire troops who have witnessed more horror in 1 hour than most people witness in the entirety of their lives.
He didn't "shout any arms back on"

but:
- Cota asked "What outfit is this?" Someone yelled "5th Rangers!" To this, Cota replied "Well, God damn it then, Rangers, lead the way!"
and
- "Gentlemen, we are being killed on the beaches. Let us go inland and be killed."
and
- "There are only two kinds of people who are staying on this beach: those who are already dead and those that are gonna die. Now get off your butts, you're the fightin' 29th."
are remembered (by the men who were there) because they did the equivalent of restoring Morale HP or Psychic Damage or convincing men to fight on despite their physical (sometimes grievous) wounds, along with his presence and willingness to shout them amidst a cacophony of artillery and high caliber machine gun fire, and inspired men to stand up and fight in the face of utter annhilation (despite pretty much everything going wrong in the operation) and win the day.
Reading all of the posts invoking "sensibilities" reveals that the Warlord issue is just a proxy war over HP as meat exclusively (or at least almost wholly) versus HP as amorphous, abstract, ablative resource to facilitate varying genres. Due to its inherent interpretation of HP in accords with the latter camp, having a Warlord in a book ....even if the "HP as meat exclusively" table doesn't have to touch it with a 10 foot poll...and it facilitates genre preferences for the 2nd group of which the 1st group will never have to interact with...affects those in the "HP as meat exclusively" camps' "sensitivities" enough that the 2nd group can't have their complete play experience (of which this malleable HP interpretation is fundamental to) because those "sensitivities" must be paramount in all phases of the design ethos of 5e. Unity edition indeed.