Right, but all are quite distinct in play experience, in narrative, in ways that a lot of suggested new classes struggle with.
The Sorcerer & Warlock? Not by half. They're arbitrarily-different mechanics for the same basic arcane-caster concept. Archetypes could have as easily separated the Wizard into book-learner arcanist, innate sorcerer, and pact-learned warlock.
Psionics, in stark contrast, have an entirely different source to justify different mechanics, and a list of wild talents, disciplines and sciences instead of re-cycling the same spells.
That's the challenge, of course - we need to get very specific about why "I grant an ally the ability to move" is not "modeling tactics" or "coordination",
why "I cast charm person" is not "I am a telepath who manipulates them into liking me with my brain." That's a challenge that most discussions I've had sort of peter out on. It's easy to say "using a magic item is not the same as casting a spell!" but it's harder to articulate really how or why, or when it's possible, it so far has wound up being something too small and fiddly to really build a whole class around like "well, the rest of my party members could use it, too."
The main reason is that the game has already gone there. It's already used arbitrary mechanical distinctions to differentiate existing classes. It's not an effects-based system where what you accomplish determines the mechanics, and how you do it is just fluff.
Another reason is that they're often far too little. There are mind-affecting spells, for instance, but there's nothing like 1e/2e psionic combat, which goes far beyond trading Charm or Dominate person spells, in both scope and detail. The things the battlemaster does with it's maneuvers /are/ like a few of the things the Warlord does - maybe 3 out of the hundreds of things the Warlord did in 4e. Say that means you don't need a Walord is like trying to say that having a Rogue with Expertise in Arcana and a Feat that gives him some cantrips means you don't really need the Wizard, Warlock, or Sorcerer (and, really, if you have one of the three, you don't /need/ the other two, but we've got 'em anyway).
And I'd challenge those fans to point out the mechanical distinction and -- the kicker for mechanically indistinct classes -- see if that distinction is enough to build a defining mechanic around.
Obviously, a system of attack & defense modes, disciplines and sciences all powered from a pool of psionic strength points would more than adequately meet that challenge. And has been doing so since 1978. Psionics has been different enough to rate mechanical distinctions in every other edition, as well - even 4e, which, until psionics came out, kept everyone on AEDU.
The idea that a Wizard MUST BE a shy, retreating, bookish academic who faints at the sight of blood (and so cannot wear medium armor or carry a hammer or learn how to do manual labor like an artificer!) or that a Fighter CAN'T BE a charismatic, persuasive leader of troops, or that a Monk is NEVER a contemplative, introspective, transcendent magus. I'd challenge those prejudices before I rolled out a brand new class.
The Sorcerer and Warlock would fail that challenge hands-down. Get over the idea the Wizard must be bookish, and a 'wizard' with inborn power or a pact is no problem.
The Monk would seem to have already met that challenge, since we have elemental and shadow monks tossing spells, or at least spell-equivalents around.
But, no matter how thoroughly you try to open up the /concept/ of the fighter, the design is too inflexible for it to be anything but a high-damage multi-attacker. That vision of 'best at fighting,' just leaves too little juice left over to do anything else well. Either that or you'd have to re-examine the whole paradigm of what the combat pillar is worth, and admit the fighter is egregiously under-powered (under-versatile or under-competent, perhaps) in the grander scheme of things, no matter how much DPR he theoretically has over the course of a day.
I find a lot of the time it rests on particular prejudices
Sorry for taking you out of context, here, but the exclusion of the Warlord could certainly be attributable to anti-4e and anti-martial prejudices, yes.