Again, let's ask the Paladin and Barbarian why they need to be separate classes from the Fighter.
Because, frankly, you couldn't get a Barbarian, as it is in 5e, using a fighter chassis. Paladin? Nope, still not going to work. At least, not the way 5e fighters are written. So, there is a pretty good reason why we get paladin and barbarian as full classes and not sub-classes. You could get something barbarianish or paladinish using a subclass, but, it's going to be missing a lot.
Nothing at all, in and of itself.
But if you're going in with the intent of playing Genghis Khan such that the rest of the party have to always do what you say 'cause you're the leader and they ain't, good luck finding people to play with.
I play most Fighter types with the intent of taking Nameless Redshirt #52 and turning him into Conan, or a Musketeer, as a result of what he does with his adventuring career; Rangers start as nameless wanderers and if I'm lucky eventually become as famous as Robin Hood.
But if you start out already playing Robin Hood or Conan or D'artangnan, where do you go from there?
Lan-"but this game goes to 11"-efan
Who said anything about starting there? Do you really think a 1st level warlord is Ghengis Khan?
And, what exactly do you think a warlord does? Do you freak out when the cleric adds a d4 to your skill check using a Guidance spell? Does it offend you when he casts Bless? When the paladin grants you a bonus to your saves, does that cause you to leave the table?
Good grief, half the classes in 5e do stuff to other PC's without their permission. Bards automatically add healing. Paladins automatically buff saving throws. Clerics and druids have Guidance spells. A wizard has a dozen or more buff spells. When a wizard grants you extra actions with a Haste spell, is he telling you what to do?
So why on earth would, "I grant you an extra move" or "I grant you an extra attack" ((Things that a 5e Battlemaster CAN DO RIGHT NOW)) possibly bother you?
Warlords never directly told you what you could do with your character. Or, at least, extremely rarely (knights move, IIRC, allowed you to switch places with a nearby ally, not that you were ever forced to). All warlords ever did was grant additional actions that you get to choose how to expend. I'm sorry, but, exactly what can a warlord in 4e do to directly tell another player to do? How many powers in 4e forced another player to do something? By the tail end of 4e, there were something like 300 warlord powers (give or take). I'll bet dollars to donuts that less than 5 of them actually forced an ally to do anything.