First?
Change the freaking name.
My beef with psionics is nearly entirely a flavor issue. Way back when I first heard about the existence of psionics, before I knew anything about them, way back when I first started D&D, I was opposed to them in a fantasy setting. Call it Mentalism, or Will Magic, or anything other than Psionics. I hear psionics, and I think psions from Babylon-5, telepath's from Star Trek, modern day psychics, and all in all, the psi in psionics makes me think of the sci in sci-fi.
The seer argument has been brought up before, and it's one that does hold some weight, but over-all, I find it's still not enough for me to bother with psionics. I find for those narrow roles, spell-like abilities - with their lovely lack of verbal and somatic components - work much better, and, seeing as how that stuff isn't always willed up, psionics still doesn't fit the bill. So I'll tweak the system I prefer, as opposed to the one I despise.
Astral slime doesn't much win me over, either.
Crystals? Geh. Makes me think of New Agers, not knights clad in full plate and wizards spellbooks.
Heck, even in settings where psionics have a semi-appropriate existence, I strip them out. My favorite setting is easily the Scarred Lands. However, the Slarecians, with their alien, almost Spelljammer-esque tones to them, and their sci-fi related cousin of an optional rule, psionics, have all been shoved out of their extraplanar airlock and forevermore shut out from my games, in all but a few, well-screened instances.
I also find psionics, in general, smacks of evolution. While I'm a believer of evolution in the real world, fantasy games I run are quite strongly in the creationism camp. I do, actually, make some use of psioncis - but never as a player optional thing, unless I'm allowing them to play monster races. I'm fine with psionic mind flayers, because that's their thing, they all can do it, it's a part of them. Humans, however? Eh...no. They don't have hidden potential waiting to be unlocked, at least in the way of supernatural abilities. Where gods and devils hold sway, the idea of evolution, or inferences to it, get kicked into the trunk.
Clutter is another reason. I don't need two separate magic systems working in the same setting. Before anyone pipes up with clerical and divine, those are still fairly similar. No power points, no manifesting, and no floofy crystals. If I were to integrate psionics in some way, I'd prefer it were more along the lines of Evocation and Abjuration; more a school of magic, as opposed to its own entirely different, special sort of system.
What would get me to allow psionics? Probably enough that the person who wanted to convince me to let him play a psion, or make them a regular part of my games in any capacity, wouldn't want to play the character, or like the addition to my game any longer.
A bit broken up, a bit scattered, but there you go.
