And a warlord playstyle is almost entirely different from a 5e bard, paladin, or sorcerer. The only way you can say they do the job is by a very vague reading of the fluff - and then pretending there are no mechanical consequences of spells being spells.
The fundamental problem with this specific assertion is that the warlord doesn't exist.
Again, this isn't 4e , this is 5e. Aside from a 1-to-1 translation of warlord being clunky and overbearing in 5e, the warlord's abilities have, indeed, been displaced about the various different classes and would suffer from lack of identity.
Bards inspire on the battlefield, heal from a distance, augment other character's attacks, and have some shared martial aspects.
Paladins incentivizes cooperative play through their auras, stand resilient when faced in melee, and are able to protect others from a distance
Sorcerers remain in the backline while controlling the battlefield but are more resilient than most other fullcasters. They can do great damage from a distance while also providing some of the best support abilities in the game.
What is Warlord doing that's unique to any of these three classes? While being a mix might sound okay since paladins are considered a mix between cleric and fighter, the reality is that its actual gameplay differs wildly from either two.
Also, it should be noted that I am not against Warlord actually being in the game. I've never been. But I am opposed to bloating the system with classes that have no mechanical design space to exist. Its fine that people want to marry theme and mechanics, that's just good design, but I don't want the theme of the class to be so unoriginal and unnecessary as "Better Battlemaster" or "nonmagical paladin" that the design turns from something fun to play into something that's just there as fanservice.
Ive never played a class for its theme, ever. To be quite honest, I don't like the overall theme of D&D as a whole. But I enjoy D&D for the mechanics that it has and how they are structured, even if it has a few hiccups.
For one, if it wasn't for Font of Magic, I wouldn't play Sorcerer at all. If Wizards had FoM, I'd play them rather than sorcerer. If it wasn't for cleric's spell list and specifically the Life domain, I wouldn't play clerics at all regardless of the themes. If it wasn't for Bardic Inspiration, I would have enjoyed Bards.
And this is the meat-and-potatoes of my argument:
As of now, there's no spotlight that the Warlord isn't trying to take away from other classes. There's nothing in this proposed Warlord class that makes me say "Wow, they'd play very differently from any other class, maybe I'll try them out."
This Warlord class has yet to show anything else but the bitter feeling of players who wanted a class they enjoyed from a previous edition brought back into the current edition. There's emotion but there's no tangible essence involved. Instead of making a Warlord, we're making arguments about its identity and what we really saw in it. But a modern Warlord that works successfully probably won't be the 4e warlord, unfortunately.