There is no functional need for a Warlord Class, evidently from the success of 5E which does not include one.
There is no "functional need" for any one class, race, or other option. That doesn't change the fact that you cannot achieve the functionality of the warlord without jumping through a lot of hoops that people would not be okay with jumping through to create a paladin, ranger, or any other class.
The D&D game designers don't think so. Neither do I, or other people. I think that taking the Battlemaster concept away from the Fighter Class deny the options and potential leadership aspects of the Fighter itself. I like having a more strategic option under the remit of the Fighter Class and reject the need for a new Class just to cater for one aspect that is handled well enough - for my tastes - under the Battlemaster Subclass. If I wanted to enhance those aspects I wouldn't feel any problem with multiclassing or taking Feats accordingly.
I'm not talking about removing the Battlemaster concept or options from the fighter. The Battlemaster's concept and options are right there, in the PHB. Adding a warlord class does not remove that concept and options from the Battlemaster. And, it's not as if class overlap doesn't already exist; just for example, there's plenty of wizard and sorcerer overlap.
I like having a more strategic option under the remit of the Fighter Class and reject the need for a new Class just to cater for one aspect that is handled well enough - for my tastes - under the Battlemaster Subclass.
As mentioned above, the existence of a warlord class removes nothing from the fighter class. And, if a warlord class were to be published by WotC or others you could easily ban it, or you could mine it for other goodies to potentially add as maneuver choices to the Battlemaster fighter. It appears to me that the creation of a warlord class is a win-win for Battlemaster fans, especially if those fans don't want inspirational healing to be part of their Battlemaster, because it definitely should be part of the warlord.
So again, you've pointed out that the options are there - just not to your taste.
Then the ranger and paladin should not exist for the same reasons. Splash some druid in your fighter, and possibly some rogue, and you have a ranger. Splash some cleric in your fighter and you have a paladin.
It ought to be noted the Ranger and Paladin were originally subclasses of Fighter too, but they have become ingrained in the culture of the game to the extent that their inclusion as full Classes is both popular and uncontroversial. The same is not true for the Warlord - for a whole heap of reasons that keep being brought up in circular arguments again and again.
Publishing the warlord as an entirely optional class that can be banned by those who don't want to use it is also uncontroversial. Now, someone will inevitably say that they don't want resources spent on the warlord when they would prefer other things be developed. However, that doesn't make the warlord controversial. The spending of resources to develop one thing at the expense of being able to develop another thing concurrently is not unique to the warlord; it is a fundamental aspect of developing all game material. In that regard, the warlord is no different than the artificer, or the psionicist.
Also, how do you think things become ingrained? Over time. The warlord hasn't had much time, a little over eight years, but it has already earned a very loyal following. And that's rather impressive considering that it didn't originate as an objectively more powerful subclass of fighter the way the paladin and ranger did.
Furthermore, as has already been pointed out, there are less-popular options and equally niche options that were included in the 5e PHB. The 5e PHB has tinker gnomes (i.e. the rock gnomes in the PHB). Tinker gnomes are incredibly polarizing; everyone I've seen on forums either loves or hates the little buggers. The warlord is easily as popular as Tinker Gnomes as a PC race.
Now, I'm not deluded. I don't expect WotC to develop a Warlord class; they clearly either don't care to cater to fans of warlords, or they don't see the onerous nature of creating a warlord-esque character in 5e. If a warlord is to be published, it will likely be from a 3rd party. Frankly, I'm expecting a lot of the material that I want for 5e to be developed by a 3rd party instead of WotC. And that's fine. Or, at least it would be if WotC would get off their collective derrieres and finish and implement a good license.