You couldn't really fake any of the main classes I was talking about without heavy modifications.
You didn't actually mention any, you just said 'other legacy classes.' Other classes besides the Warlord, from past-editions Players' Handbooks would include the Knight, Psion, Shaman, Avenger, Warden, Beguiler, Invoker, Ardent, Battlemind, and Duskblade, IIRC.
The Knight was a slightly sticky non-casting tank, a protection fighter fakes it reasonably well, add a Noble background for the non-combat. Psion could be the afore-mentioned GOO warlock. The Shaman was a nature-oriented Leader in 4e, the Druid covers that in 5e, not wonderfully well in terms of fluff, but better in functionality than a BM or PDK covers the Warlord. The Avenger... Acolyte Assassin gets the unarmored and divine aspects, but would be pretty short shrift, a Rogue sub-class might cover it, though. Warden is conceptually covered by the Oath of Ancients Paladin, but was a Shapechanger, which'd be Druid, maybe MC the two, but the Paladin at least is in the right ballpark, functionally. Beguiler, not familiar, don't see how an enchanter or other arcansist with the right spell choice would be far off. Invoker, the blasty alternative to the 4e Cleric, the 5e Cleric can be plenty blasty. Ardent? If you hate psionics = magic, about as bad off as the Warlord, otherwise re-skin the support caster of your choice. Battlemind... OK, nothing much resembling that, I'll grant. Duskblade, bladelock, I assume, or one of the other gishy sub-classes, Bladesinger or EK.
The closest is maybe Spellthief, but that's condensing an entire class concept into a single, extremely high level ability. As far as I'm concerned, Warlord is way better supported in 5e right now than Spellthief.
You are talking Core class vs complete adventurer oddity, there.
I'm not trying to speak for anyone other than myself for why a dedicated Warlord class is low on my own personal wishlist. And my reason is that Warlords basically already exist, just in an unrecognizable form from the 4e version.
OK, you're only speaking for yourself, but it's an odd context if you're merely indifferent, why aren't you boosting the class you'd like to see - like the Spellthief in the UA thread about Rogue subclasses - or did you, I can't confess much interest in that thread, so don't recall it too well?
Which is the dirty secret about converting 4e classes to 5e; you can't. I mean, you can obviously, but in 5e terms you either have to give it full spellcasting, including cantrips, or you have to trim a whole hell of a lot out of it.
Heh. Converting 4e classes verbatim would be problematic, as would be shooting for the same kind of balance as 4e achieved, sure. 5e simply doesn't approach class design that way, though. Look at how very different the 3.5 and 5e Sorcerer are, mechanically, for instance - or rather, how different all the other casters /aren't/ from the 3e Sorcerer, since they all cast spontaneously! That mechanical identity was gone, but they kept the whole power-in-the-blood thing, and at least made it a full class, even if they didn't have much to offer it in terms of uniqueness. It's design from the concept out, not build within a functional box. The Warlord concept was constrained in 4e by Role, in 5e, a lot /more/ could be done with it.
4e characters could simply do a lot more things, a lot more often, than 5e characters.
Well, than 5e non-caster characters. The reverse is true for casters, an Epic 4e Wizard would be dumbstruck by the power of a 5e wizard, even one half his level. More spells known, more spells ready, more spells per day, all of them more powerful, just /MOAR/. ;P The casters 5e tackled had traditional incarnations before 4e, and that's what 5e harkened too. Again, the Warlord concept isn't held back by any such baggage.
This is why WotC will never be able to make Warlord fans happy, despite giving them the class twice (just under, frankly, better names) as fighter archetypes.
See, that's just sad. The BM was a sad, failed attempt at a 'complex' 4e fighter. It's less a Warlord than an EK is a Wizard - a lot less. The PDK is a Cormyrean PrC.
5e characters simply do less than 4e characters do, and less often. Even spellcasters, really. Well, inside combat, anyway.
OK. 4e Wizard. Level 1. Knows two dailies, can prep one. Has 1 encounter. 2 attack cantrips. 5e Wizard, level 1, Knows 6 daily spells, can prepare 1+ INT mod of them, can cast 2 of them per day, including casting the same one twice (which the 4e wizard can't do until high level), and can recover one of them after a short rest. The gap only widens from there. Don't even get me started on the Druid. I was a big fan of the 1e Druid, the 4e Druid was a disappointment, the 5e an embarrassment of riches by comparison.
But nobody complains about recreating the 4e Fighter. Or Rogue. Or Barbarian.
Heck, I still wish 5e could handle the 3.5 fighters I liked.

(I'll grant I couldn't care less about 4e Rogue or Barbarian, just not that into 'strikers,' myself.) But, the 4e Barbarian with his spirit connection just got a little more half-hearted support from UA. So it's not all bad on that front.
Any new attempt at a 5e Warlord would either be a hodgepodge of what we already have, and it would still wouldn't be good enough, or, at best, a new set of abilities that still would represent a very limited amount of the things the 4e Warlord could do. At best, it would be an interesting class that would almost certainly get torn to shreds.
IDK. Some of the classes in the PH were well done. They weren't all Sorcerers and Rangers. I can't pretend to have a lot of faith in WotC at this late date, but I'm willing to give them another chance. (Not a 'second' chance, mind, it's not like I'm even counting at this point.)
Personally, I'd rather see something new.
Like a support class that doesn't rely on spells? A non-magical class that can do a variety of things besides damage?
That would be new.
The Warlord was the newest thing in D&D since...
... I really don't know. D&D was so stodgy prior to 3e. Modular multi-classing or Feats, I guess? ...wow, that's kinda a depressing thought, really....