D&D wizards have pretty much every superhuman power going - invisibility, shapechanging, curses, teleportation, mind reading, superhuman strength, etc - with healing and protective stuff going to the cleric. So in terms of effects, of end results, you don't need much more than a wizard. But in terms of the way those end results are generated - spellbook, memorisation, Vancian periodicity - D&D has been very limited for most of its history.
So maybe what people are looking for with psionics is not new effects - there's nothing new there anyway - but new means of generating those effects - spell points and the like.
I would agree. But lets say we did have a generic system of magic divorsed from spellbooks and Vancian preperation, then that system would be equally applicable to 'Wizards' or 'Psions'. When you get down to it, Wizards as we normally think of them coming from a D&D background and the consensus modern fantasy tropes it helped to create are just guys that study, mediate, and prepare their minds to create physical effects through the force of their will. And, that's a fairly adequate description of 'Psions' as well. The only differences we tend to pay attention to are whether you accomplish that with a little help from chanting, arm motions and the occasional ball of bat guano, or whether you've got a bunch of cystals and similar foci. But its worth noting that crystals and similar foci are themselves just the trappings of a certain style of magic, and the reputed magical properties of crystals was listed in the 1st edition DMG.
As you say, Celebrim, the scope for new development in D&D is other means of generating effects such as true names, summoning spirits or whatever.
I personally feel that redressed, the 3.0 era Sorcerer is a pretty darn flexible and fairly generic class capable of emulating just about any magic user of any sort in fiction - including Psions (whatever 'psion' means, which is not clear to me at all since historically 'psychic' powers are just magic).
Granted, its not capable of emulating the highly open and flexible spellcasters of certain RPG systems, but its to me not at all clear that those systems actually do a good job of emulating magic users of fiction or myth. There are alot of reasons I feel that, but the basic evidence of that is that games featuring open ended flexible magic never in practice play out like the magic users of fiction who are almost always in one way or the other more limited in their actual application of magic. Magic users of fiction almost always find a way to only have access to just enough magic to accomplish the plot. Rarely do you see them display open ended continual power; even in a series like 'Wheel of Time' or 'Avatar: The Last Airbender' where it seems to be implied, there are always plot reasons why that awesomeness isn't going on all the time. Players rarely feel themselves so constrained and so unwilling to change the world when they have access to phenomenal cosmic power.
To handle this, open ended magic systems must either accept that the players are veritable magical demigods right from the start, or else must severely limit the power of magic. But neither solution seems to me to actually emulate the magic of most fantasy fiction, which seems to allow for amazing world changing effects just not necessarily 'at will'.
To me, much of what is wanted in 'Psionics' seems to me highly circular. People seem to feel that it feels 'psionicy' if and only if it has a certain mechanical system, but that that system to me seems solely a game artifact. To be perfectly honest, when someone says that they want 'Psionics' in a game, beyond the request for a certain mechanical system I have absolutely no idea what they mean and I'm not sure that they do either.