As for the others, you are casting your net very wide.
Charismatic Warrior Hero is a pretty broad archetype. There are /many/ examples.
It basically includes any hero with a charisma over 10 and/or proficiency in Persuade. The idea that they should either be a battlemaster, a bard or a paladin is silly. Conan is a barbarian. Jon Snow is a ranger.
You're presuming a conclusion.
Archetypes and characters from fiction don't have D&D CHA, and aren't a D&D class - they are what they are - D&D can be used to try to model them by choosing stats, race, class and so forth.
And it can often model them poorly, or inefficiently.
Respectfully, ALL characters receive a great benefit from a high charisma.
Which means those universal benefits, have no bearing on weather a given class is a good choice for a 'Charismatic' concept.
When we are specifically talking about what makes a good party leader and hero who inspires others through words, the most important thing *IS* perficiency in persuasion and a high charisma.
Exactly what does that do to inspire his party? PCs aren't mind-controlled by persuasion, so how are you leading, exactly? How does that compare to doing the same things with CHA & Persuasion /and/ giving them a nice bonus to saving throws?
Except that the fighter shouldn't *have* a low charisma first place if you are actually rolling a character of the sort we are talking.
The question is should you be rolling a fighter, at all if that's the sort of character you want to play?
The fluff of Battlemaster and PDK certainly imply it, but the mechanical support is slim compared to the Paladin or Bard.
I definitely agree that by base classes alone the fighter falls short of the paladin in terms of being a party leader or party face, but once again, the extra ability score increases mean getting inspiring leader and whatever other feats you need
Actually, it's more like getting you second feat 2 levels early. But, the OP maximized the impact of the fighters bonus ASI by specifying filling the concept /at 6th level/.
No. It isn't. The question of what is "best" for d&d is subjective and entirely dependent what someone finds appealing and fun, and even minmaxing can have different goals in mind.
Its really pretty straightforward. Any class can max CHA and take persuasion, the, question is, what are the consequences and perks of doing so /for that class/.
A wizard prioritizing INT over CHA is a worse wizard, and gets nothing in return, a Bard, Sorc, or Warlock doing so is the best caster they can be.
So it's just a practical look at mechanics.
The other options, bard and paladin, both come with either being a full caster with less health/lower ac,
And that is a strike against them, as the archetype rarely evinces supernatural powers, let alone casts spells.
You also seem to be under the misconception that charisma is useless to fighters, .
I am not, I pointed out that the BM's Rally Manuever leverages CHA. It's just a really small amount of leverage. If you bring in feats, and thus Inspiring Leader, it becomes almost trivial by comparison.