I only remember two 1e psionicists. Both were rangers, and due to the nature of psychic combat, they would usually lose and go unconscious in the first split second of a fight. This lead to many jokes about narcolepsy. I had a player try a 2e psionic halfling, right after the book came out, and mainly just to try it. He was the hero of the party at first level...then quickly became the goat as it became apparent that he was just plain better than anyone else.
I can't say I've had any experience with the 3e or 4e psionics. I bought the 3e book, but exactly zero players were interested in playing one. They were commonly forbidden amongst my gaming circles in 2e, but I never had to ban them in 3e since then as they weren't mentioned except as a joke. (I haven't run or played 4e since they've been out.) The basic problem, as I see it, is that Psions are practically the same as wizards (filling a similar narrative role), but somehow always want to be different.
As far as whether they should be anywhere near the core....maybe in a module, but not the basic game. I guess it depends on how they do it.
A) Psions are a specialty mage/cleric thing. - I would be okay with this in a module about specialty casters.
B) Psions are a different class, but follow the model of other casters using default 9-levels of Vancian powers, with feats to get at wills or other mods. - Wouldn't be bad...but why bother? They would need to be very distinct in flavor and form from wizards, which is unlikely. Otherwise, just talk to your DM about flavoring your Wizard (or priest?) to hold his temples and squint when he casts instead of the normal shenanigans
C) Psions are a different class(es) and follow their own wonky mechanics. - I would not want this in basic/core, unless those wonky mechanics are the point of the module and extendable to other casters. Giving them their own special mechanics makes both the mechanics and abilities much harder to evaluate beside other classes and their abilities. That makes it much more likely to have psionicists seriously mis-powered compared to other characters. If they are to get their own mechanics...I dunno, put it in Dark Sun or something as a special campaign world book.
Additionally, for me, any of the three options can be made unpalatable with the inclusion of the idea that Psionics is somehow "not magic". The one guy babbles in an obscure language while wiggling his fingers and holding a staff....he's a wizard. The other guy clutches a holy symbol and beseeches some god for juice...he's a cleric. The third guy clutches a crystal and stares creepily...he's a psion. They all make weird/impossible things happen by performing apparently unrelated acts....i.e. magic. As far as I'm concerned, the idea that psionics is some kind of of uber trump magic needs to die in a fire.
That said, the inclusion of Psionics in the PHB core wouldn't stop me from buying it...or forbidding it in my games (if I see fit, who knows it could be awesome.)
