Absolutely true. But that's a completely arbitrary benchmark.
Mearls chose it, FWIW, and it is decidedly symbolic of including fans of all editions.
But I could say the same thing about a myriad other concepts, many of which are as iconic in fantasy if not more iconic than the warlord.
Like the alchemist. Or the dedicated shapeshifter. Or the summoner. The The elementalist. The shaman. The pirate. The witch doctor. The tinkerer/engineer. The inquisitor.
None so prevalent in genre as the heroic archetypes modeled by non-casters like the Fighter, Warlord, Rogue or Barbarian, but mostly found in genre to some degree (if rarely as heroes). All have been classes (if we include NPC 'classes' & PrCs), and all could stand with some treatment going forward.
The sorcerer was in two PHBs: 3e and 4e.
PH1 was where Mearls drew the line, and the Sorcerer was only in the 3e PH1, not the 4e PH1. The Warlock and Warlord only appeared in a PH1 in 4e.
Mearl's criterion was an early goal. And he was quick to amend that the options might not be classes.
Sure, the Illusionist & Assassin, for instance, had always been sub-classes and were in 5e, too.
I personally think there probably is room for tactician and strategic planner class. But that may or may not overlap with the leader role depending on how the player wants to portray their character and what role in the party they want to fill.
Obviously there's no formal leader role in 5e, there's classes - Bard, Druid, Cleric, Paladin - that make a lot of support contributions, which map to that formal role, though they go far beyond it, as well. The Warlord (strategic/tactical/inspiring &c) would naturally make those sorts of contributions, and, to be a viable class in 5e, would have to be more flexible, as well.
I don't think that being invested with authority is sufficient to establish a character as inspiring to his/her fellows. The history of the world is full of formal leaders whose underlings followed their orders out of simply duty rather than love or devotion.
Not to mention those who were just plain bad at it. The combination of authority to lead /and/ the skills & talents to do so well often results in a 'great leader' or hero who stands out in history.
In 4e, PC development has a certain trajectory that makes this LotR-style character development easier to bring out in the game. Because of the transition from heroic tier to a paragon path to an epic destiny, a warlord PC's destiny of being a great ruler or leader can emerge as the game unfolds: eg at 11th level the warlord PC becomes a Knight Commander, retrospectively vindicating his/her earlier claims to be a leader; and then at 21st level s/he becomes a Legendary Sovereign.
I think that 5e doesn't build in quite the same trajectory for PC development, so there is perhaps a greater risk of a 20th level warlord not having progressed much beyond 1st level in terms of character backstory revealing how and why the character is an inspiring leader.
There's no PP or ED, but 5e does still go through Tiers, and the idea of higher level characters creating a Legacy that was floated in the playtest needn't be dead. It might be years before some supplement comes out to expand upon it, but it could happen.