That's not what a theme is. Psionics is not a theme (much less the theme--seriously?!?), defiling magic is not a theme, sorcerer-kings and lack of metal and desert wastes are not themes. They are setting elements, which support the theme in various ways.
The theme of Dark Sun is a ravaged world sucked dry by the wanton abuse of its environment. Psionics elaborates on that; it shows how the inhabitants of Athas have adapted to scarcity and hardship. Deprived of all but the most primitive tools and weapons, they have found ways to use their own minds to compensate.
But nothing in that requires professional psions. Rather the opposite, in fact: The salient feature of psionics on Athas is its widespread amateur use. It's the "everyman" power, the answer of the masses to the elite wielders of magic. The typical Athasian psion is not a wise ancient master but a street urchin who can pick pockets from thirty feet away, or a farmer who can sense water deep below the desert surface. You can have the professionals if you want, but the wild talents are far more important.
"Well, y'know, Eberron added in their little Magewright NPC class to represent how common Arcane Magic is, and there's feats and subclasses. So a 5e Eberron doesn't need Wizards!"
That's how your post reads, Dausuul.
Yes. Psionics is widespread in Dark Sun. Many monsters and characters have minor quantities of it because it's just -that- ubiquitous.
But there are Psionicists core to the setting. The idea of the Will and the Way being a potential path to power. Not just some one-off thing. Of characters who focus their minds into powerful weapons and become more than just "A Gladiator with a Psionic Trick"
Now you -could- be ridiculous and make a "Separate from Class" Psionic Progression. Or make psionic subclasses for every single class in the game and -call- them Psionicists...
But that would be up there with pulling Wizards and Sorcerers out of Eberron in favor of Eldritch Knights, Arcane Tricksters, and Magewright NPCs.
It wouldn't encapsulate what a Psionicist is, would take far more effort, and be incredibly frustrating to the players who actually want to play Psionicists rather than refluffed Wizards.
And Dark Sun? It would not be Dark Sun without Psionicists.
And that's totally fine. You wouldn't like my Dark Sun, which has smaller psionically powered classes instead of a psion class, and makes numerous lore changes (no more Cleansing Wars). But I would disagree if you told me it wasn't Dark Sun; it has the same map, has sorcerer-kings in isolated city-states, defiling arcane magic, and a focus on gritty survival in an unforgiving desert. That's Dark Sun enough for me.
Yeah... Dark Sun enough for you... but not Dark Sun from TSR or WotC. Homebrew seriously altered Dark Sun. Not the full package.
If they put out a full package, it needs the Psionicist. Your table aside, the setting and the history call for it.