Let me just. Dredge this up
Psions absolutely are spellcasters. In fact, pretty close examination of them finds they have exactly the same lore as wizards with just some very minor variations in the costuming. This is hardly surprising since in the real world "psychic" was just traditional wizard-y magic redressed in a pseudo-scientific garb to try to give it some legitimacy, and it is actually "psychic" and not psionic that is the origin of D&D psionic tropes. I mean it's as big of a misnomer as "longsword" and "plate mail".
That they have different mechanics is a result of the tacked-on nature of psionics in 1e AD&D. It has nothing to do with the lore, and everything to do with player expectations of having a mechanical system that isn't spell slots.
No, psions aren't spellcasters. They're psions. Psychic stuff is closer to sci-fi as a 'this is what humanity becomes' type of deal. The original term may be different, but nowerdays its going to refer to a different thing, the whole reading minds, controling other people with your thoughts type of deal. Or, y'know, Mewtwo from Pokemon.
D&D's wizard is very specifically 'You have a spellbook and you cast these spells' type of deal. That isn't how psionics are displayed so I don't know why you've said they have the same lore because like... They demonstrateably dont? Amuro and Char from Gundam (Pick your favourite Gundam protag here, they're all basically Newtypes, except Domon who's the resident martial arts expert) doesn't lug out spellbooks, they're just naturally psychic (well, newtype), naturally got that whole link thing going on with other people, and can just push their respective mechs well beyond what they were desigend to do because of that. Mewtwo from Pokemon doesn't cast spells, he thinks and all of a sudden the joint is exploding all around him and he's doing shadow ball. Hell, Mewtwo we have the exact "He isn't a wizard" comparison because if you're gonna tell me that Mewtwo plays like the most Gish (there are no pure wizards), Robin, we're going to have to have Significant Questions.
Here's a fight of two Ex ones of them going, are you actively saying these are both wizards? Tassadar from Starcraft (or heck, the entire Protoss force) don't cast Thought Talk or whatever, they can just project voices into other people and have a psychic link between them all, and merge together, sacrificing their flesh and blood to become huge, terrifying storms of energy that decimate my precious zergling hordes
The wizard, and hell the Magic User entirely, fails miserably at invoking what people want the psion to be. It has everything to do with the lore. It has everything to do with player's expectations at what a psychic character should be capable of. D&D's psionic tropes exist because of the larger use of psychic powers in fiction. Heck, the whole pyrokinetic stuff is just Carrie
We've seen what happens if you remove psion anyway in this edition. People just, invent a new one. Over and over. Multiple times. Because all of the attempts thus far have failed to scratch that itch, and wizard certainly ain't doing it. Didn't do it in 1E, and certainly hasn't done it now.