It does seem like dragging up the past from a divisive edition war, that happened in the 5E playtest, so I'll try to tread lightly. The Warlord class had several problems:
1/ The name 'Warlord' is actually a pejorative title, in terms of it's origin. I guess you could argue that 'Barbarian' is too in a way, but Warlord also denotes a certain rank which, at Level 1, hasn't been earned yet. It's not as if a Level 1 character is talking his/her war-horde on adventures, and the other PCs should not be assumed to be the subjects of that character either. You could argue that the name is superficial and could be replaced - that is what the 'Battlemaster' tried to do in 5E. It is possibly a bit of a bland name too, but the concept is there at least.
2/ Having a distinct Class put aside for a Warlord is problematic as the actual reason for it's existence is mainly to fulfil a mechanical niche ("I want a non-casting healer" and so on), rather than a narrative one. People may suggest things like Alexander the Great (above), but he's a Fighter (who has obtained a certain high rank or Level, and accrued a leadership role accordingly). If you create a seperate Warlord Class, all you are doing in effect is stepping on the shoes of the Fighter Class. That's why they made Battlemaster a sub-class of Fighter - to give an option to build Fighters that weren't just one-trick-only meatheads.
3/ The rules to make a Warlord type of character are pretty much there if you want to, in 5E. I've had debates about this before with Warlord fans who have argued some very specific details about the previous 4E class that I'me not fully aware of (I didn't play 4E much, as it didn't suit my tastes at the time). However, in the context of 5E alone however, you can build a character that plays that role with a Fighter (BattleMaster), maybe a Noble or Soldier Background and a judicious use of Feats (Leadership or Healer, etc) or maybe even a level or two in multi classing (Bard: Skald) if you want. You probably want to put higher stats in Charisma or Intelligence than a stereotypical Champion style Fighter, but it's doable. You don't need to design an entire new Class to do it.
4/ As alluded to above, and like it or not, the Warlord Class is symbolically tied up in the issues people had with 4E. It became a focal point for conflict at the time. I'm pretty sure that WotC want to avoid that conflict again.