Limit Break Dancing
Alas, this is the Internet, and discussions usually devolve quickly into "you're wrong and I'm right, which I will now explain in an unnecessarily hostile and insulting manner."Dark Sun doesn't actually need psionics to be Dark Sun. Ultimately, the role of psionics in Dark Sun is to provide character options, but psionics don't directly address the central themes of the setting. You can have a perfectly cromulent Dark Sun game without psionics at all. It's not a necessary part of the setting, and the thing most easily severed from it without much change. I know, I know, lots of people liked psionics in Dark Sun, but it didn't define the setting, it just let you have wizards that didn't trip over the arcane magic is bad detail, or clerics when there were no gods. Peel off the psionics and your still left with an extremely flavorful setting with lots of room for play. Add it in, and you have pretty much the same thing just with some different character options. In fact, to say another bad thing, given how badly screwed wild talents could be in psionic conflicts in pre 3e D&D (I didn't do any Dark Sun post 2e), it might even be beneficial to avoid psionics in Dark Sun for non-psions/non-lucky-as-hell characters.
Anyway, I've said the horrible thing, now it's time to argue about it. Discuss.
But I agree with @Ovinomancer: Dark Sun doesn't actually need psionics to be Dark Sun. "Peel off the psionics and you're still left with an extremely flavorful setting with lots of room for play." Which is true. I mean, it's fiction; we can add/remove/change it to suit our own whim.
"But then it wouldn't really be Dark Sun!" some might say. They'd be as correct as they wanted to be, but I'd be too busy playing it to argue.