The debates about psions as casters involves another secondary debate, which is rarely pursued clearly and directly, about what we think mechanics are in narrative terms. It's alluded to in some of SteamPunkette's discussion above, but I think it's worth getting out more clearly:
Sometimes we talk about having psionic powers represented by spells, and other times we talk about psionic powers simply as spells. These are two fairly different ideas about the narrative implications of game mechanics. There was a time when DnD made the distinction clear. For instance, giving a gith "Mage Hand" to represent a small psionic ability didn't mean they were casting a spell. It was simply that, given what "Mage Hand," the spell, could do, it was an easy way to represent a small telekinetic talent. Other spells were put to similar use, either on monsters or on character species. In this case, the game mechanics of the spell are being separated out from the "story" spell. Under this sense of things, if a wizard casts "Mage Hand" they are using a distinctive magical formula, with a concrete place in the story-world, while the psionic character is using their telekinetic powers and "Mage Hand" simply gives an easy mechanical form for that power to follow.
Unsurprisingly, this ends up fairly confusing, and eventually it produced the idea of “psionic spells,” where spells were being cast “but with your mind.” And it wasn’t unreasonable, under those circumstances, to don't we just think of the psion as "casting 'Mage Hand'"? (One could also argue that the gradual evolution shared spell lists across classes has contributed to a more general version of this confusion regarding spells/mechanics.) In any case, the current proposal for the psion pursues the second option, and this involves two slightly different ways of thinking about what spells are:
The first is the one given in the play-test materials: spells have a concrete existence in the world of the game, and the distinction is one of access. Thus the psion is simply doing magic (not some secret third thing) and calling on that magic through a different narrative route. "Fireball" is a magical power in the campaign setting, and different casters are all essentially calling up that "Fireball."
The second way, which often comes up in this thread in various forms, is that we treat spells not so much as real "things" in the world of the game, which the mechanics represent, but as mere effects. Thus, there is an effect, which involves bringing fire into the world and using it to damage your enemies. A wizard might chant a magical formula and fire from the elemental plains is drawn into a ball and hurled at his enemies. A psion might concentrate on the latent energy in air, exciting the molecules with his mind, until the room erupts in a ball of fire centered on his enemies. Two different activities in the story, but “casting ‘Fireball’” is a convenient way to represent the action in a round of combat, the damage it does, etc.
The difficulty really comes into play, unsurprisingly, when we talk about what we prefer. Some players are thinking primarily in terms of effects, but this often ends up eliding the two models above: “A fire ability is a fire ability, so why not just have everyone cast ‘Fireball’?” The idea that we have identical outcomes means that the story itself (ie. what is magic in your world, what are psionics in your world, etc.) is being adjusted as well.
Cards on the table: I prefer a version of the psion with a distinct suite of powers, something more like UA “Mystic” class. This is, in part, because I want the mechanics to mean in a particular way. In the game, there’s a magical formula for a spell called “Fireball.” When your wizard finally achieves enough power, he manages to scribe that formula in his book of spells, memorizes its complicated formula and gathers the ingredients, and when he’s in combat, he unleashes a fireball on his enemies. Likewise, I would like there to be a “Pyrokinesis” power for the psion, one that functions more like a skill—the psion’s ability to reach out with his mind to grasp the world and alter it in some way. If it’s a skill, then it can be honed or scaled in various ways: from setting small things on fire, to heating the metal in your enemies weapons, to making a campfire flare up, to raising the temperature in a room, to (eventually) creating a conflagration around your enemies. The fact that you can find a spell to match each of effects doesn’t mean that something distinctive about the psion isn’t lost when you simply make the psion use spells.
That is, the distinctiveness of the psion disappears to a degree that makes them not only mechanically redundant (if a wizard can cast most of the psion spells, what’s the point of the new class?) but also narratively redundant: the psion is just another spellcasting tradition in the world of the game. It’s also, I think, a problem for the narrative meaning of spell mechanics themselves. That version of “Fireball” in the previous paragraph either a) no longer names a special thing in your game world, but just names a mechanical effect available via a variety of powers. (Or, as I note above, you’ve made the psion just a mind-spell-caster.) Either way, I think you lose something important about how mechanics and story relate.