As I'm sure is a shock to no one, I'm concerned about story. In this particular case, the story of the Classes in question. The game as it stands have really only two "generic" classes-- the Fighter and the Rogue. Both of them are really more just a category name and it's the subclasses inside of them that give the flavor of what they do. But all the other Classes are tied to their stories-- how they get what they get, how they do what they do, where they come from, how they feel about things, and what is their place in the world at large. That story and flavor is a foundational part of the Class-- they aren't just a random and generic pile of game mechanics. Which is really the whole point of having a Class system in the first place.
But that means that any new Class is going to have a similar need for a foundational story. A reason for the class to be a Class. The game is not going to introduce any more "flavorless" classes like the Fighter or Rogue. The new Class will need to have a place in the world carved out for itself, because otherwise the expectation is that another Class will fill it (via subclass or slight refluffing or multiclassing.) This is exactly why the "swordmage" Class has never gained traction-- because there's never been a foundational story for this class that hasn't just been "a fighter / wizard multiclass that gets its own stuff". So because of that lack of story, the game has always just given us things like an actual Fighter / Wizard multiclass, or the Eldritch Knight or Bladesinger subclasses, or even subclasses off of other classes that fill a similar niche.
I think this is where all the stumbling blocks come from-- when the class idea's story is too close to another class's story that it seems almost a waste to make a full 20 level class for it. Like for instance, the "Summoner". We already have Summoning in the game, and several classes that do summoning. They might not
focus on it, and they might not get mechanics to be
better at it... but what is the story of a specific Summoner or Binder class that is truly different at a foundational narrative level than the classes in the game that also do it? See also the "Archer" class that I see bandied about. What is foundationally different about an Archer's story compared to a Fighter (especially considering the Fight has been built to be so generic you can put the Archer into it?) Now if someone comes back with "Well, there are a lot of archery tricks that you do within an Archer class that you can't do as a Fighter"... that might be true, but that's purely game mechanics. That person is just looking for a different mechanical way to do a class whose story is no different than what we already have. And I suspect that's why we don't ever see that get made (except by 3rd parties, or maybe way down the line of WotC's publishing schedule.)
Why do we not have a Warlord? Because Mearls and Crawford said at the very beginning that the Warlord's narrative of a warrior who is more strategic and tactical at combat is not really any different than the narrative of the Fighter, but whose focus in one on combat in a certain direction. Now there might not be enough
mechanical expression of that Fighter to recreate what fans of the 4E Warlord want to see... but story-wise there is nothing in the narrative of the Fighter class that precludes the identity of the Warlord. And that's why it was never made by WotC in 5E and who knows if it will ever be made?
The Psion? Again... the baseline narrative of the Psion is being able to do fantastical things via the power of your mind. Even laying aside the concepts of whether you call that "magic" or not (we don't need to rehash that argument)... the foundation of the Class is that the power comes from within the Psion character themself. But unfortunately, that pretty much lines up with the story of the Sorcerer too-- a Class who gets its power from within itself and not via some external action or force (gods, music, nature, extraplanar beings, the Weave etc.) Obviously the Sorcerer cannot do
mechanically what fans of the Psion (and psionics) would want to do, and parts of the story of the Sorcerer do not align to the traditional ideas of the Psion (using CHA instead of INT, using spell components, a spell list of many non-psionic things etc.) But the foundation is the relatively same-- having the power within yourself to do these fantastical things. (That being said... I think the narrative differences between the Psion and the Sorcerer are indeed great enough that if/when there is a place to create and place a Psion Class (like for instance Dark Sun), it'll get done. The same way WotC eventually decided that the Artificer didn't end up working under the Wizard chassis despite a similar narrative foundation, so they finally made it a Class on its own when they had a book-- the Eberron campaign setting-- within which to place it.)
Now of course the argument can be made that even within the 12 Classes we currently have, there are several that could be said to tread upon the same foundational story and thus you could "remove" some of them if you wanted from the game (the Druid being just a Nature Cleric but with different mechanics, the Paladin being a War Cleric but with different mechanics, the Ranger being a Fighter or a Rogue but with a nature background etc.) And I won't argue that isn't the case. The idea of the "generic" Core Four is greatly tied to D&D-- the warrior, the expert, the divine magician, and the arcane magician (and I'm sure there are those out there who would merge the divine and arcane magicians into a single class too if given a chance.) And you could certainly build the Class system of D&D from that foundation too... where the four Classes are generic umbrella terms, and then the Subclasses give us all the narrative story of what their individual places are within the world. But I think that ship has sailed. There's a reason why we hear virtually no one using just the Basic Rules to play D&D. Because the ones that want to play that style of old school I think are just going back to play those actual old school games themselves because that way they can definitely get the experience they want, rather than trying to jerry-rig 5E to do it.
At the end of the day... any Class to be added in 5E is going to need a reason for its existence as per the ideas of the WotC D&D design team. A foundational place in a world that requires it. The "Artificer in Eberron" or the "Psion in Dark Sun" kind of place. Will we get a gish or swordmage type of Class? Maybe if the designers determine that a Spelljammer / githyanki campaign setting (and book) needs it. Will be get a Warlord? Maybe if the designers determine a Points of Light / Nentir Vale campaign setting (and book) needs it. But until then? I just don't see it happening. They're leaving those things to KibblesTasty to make for them, LOL.