I'm saying its a divisive narrative that is highly likely to cause friction within a group (especially given that D&D players are still most likely to be geeks, the hereditary enemies of jocks). Also see, kender.
Friction in the party is a great roleplay mechanism. Isn't that very dispute between the intel officer and the field commander a tale as old as time? I see the flipside narrative of this all the time where people intellectually bully the barbarian with eye-roll stuff... but it is all an opportunity for roleplay on the group dynamic of people who don't see eye-to-eye. Also, this type of character has no MECHANICAL way of forcing any decisions on other players. It's like that captain you hate, but the dude knows how to spoil his team after battle and you'd rather have that prick at your back, you may ignore his douchery and do your own thing though.
Back to the warlord though..serg. Narrative is just one. And no, I don't think that is just a high charisma fighter. Like your many other magic subclasses, I feel that the innate ability to lead fighting men, make them ignore fear and screwed up crap, push them beyond themselves, or jump when you say jump - with your (charisma). Is a legit class gap that is not well-filled by just a battlemaster with incredibly limited ability slots to devote to developing and utilizing charisma (especially when they only have so many times per day that they apparently warlord it up). Again, maybe a secular warship

paladin comes close and I don't hate that close second. I would agree with you if the battlemaster came with higher quantity of charisma based buff maneuvers and amount of times they could actually command on the field it would not require its' own class. But no, narratively, commanding others at this level is an innate 'it factor' that not every fighter (even charisma fighter) would have. Mechanically, it relies on charisma, and has too little support coming from the fighter shell.... I guess you could wait till battlemaster level 15 though to have consistent access to 2 abilities that you could CONSISTENTLY warlord it up with.
The balanced shell of this is already there, commanders strike where you sacrifice your own modest strike to gift one. Protection fighting style (sacrifice DPR for a buff), a few others. But it gets pretty patchworky.