Hussar
Legend
And still not a single one needs a warlord class, over what is already present in the 5e PHB, to emulate.
But, as has been repeatedly stated, this is an impossible criteria for a class. You can make virtually anyone with just cleric, fighter, thief, wizard if you squint hard enough. There's absolutely no reason to have the other classes in the books, if "you can already make it with existing classes" is the criteria for a new class. 2e shows that quite clearly with the Kits that they had. Minor tweaks to existing classes to shape them into new archetypes.
The idea that I can take a fictional character as evidence that it can ONLY be presented as a single class, as justification for the existence of that class, is far too high a bar. Conan can be presented as a simple fighter - which he would be in Basic/Expert D&D. Or he could be a Fighter/thief if we use AD&D. Or arguably a bunch of other classes (you could make a decent argument for monk if you liked) could model Conan. Is Aragorn a ranger or a fighter? Well, depends on who you ask and which system we're using. In 5e? I'd likely go more with BM fighter to be honest. He's not an archer or a two weapon fighter, so ranger is largely out, nor does he cast spells or have an animal companion. Does that mean we should eject Rangers? No, of course not.
The bar for the inclusion of a new class, whether it's a Warlord or a Psionicist or whatever, is, "Does this class fill a niche that is largely unexplored by other classes?" You can make a pretty decent Psion with a Sorcerer or Warlock. It gets about 60% there. Yet, we're seeing a new Psionic class coming out because Psion fans want that other 40%. You can make a pretty decent Artificer with a wizard subclass, but, again, it's only about 60% there and fans would like to see a full class. You can make a pretty decent warlord with a Battlemaster or a Bard (or possibly a mix of both) but, fans want a new class for that other 40%.
The fact that you can get some of the way there using existing classes doesn't mean that there isn't room for that extra bit to make a new class. The fact that you can model fictional characters numerous ways does not preclude creating a new class.
What rather baffles me about all this is we had push back with other classes - the Psionic ones for example, but, never to this degree. What is it about the Warlord that is so objectionable? Is it the healing? The buffing? What? What is needed for a Warlord class is a slightly different chassis than the Battlemaster (different HD, no 3rd and 4th attack, less armor for instance) but using the BM's mechanics expand on what the BM can do in the game right now. The BM can already grant extra attacks, so, that isn't unbalanced. The BM can already grant some Temp HP, so, that's not unbalanced. The BM can already grant extra movement, again, so, that's not unbalanced. Granting some more of the same things will not necessarily unbalance the system, particularly if the one granting the bonuses isn't directly doing damage.