Okay, let me redirect slightly, as my point seems to be not very clear:
What central theme in Dark Sun is removed if you take psionics out, other than just not having psionics?
Dark Sun, to me, was awesome because it subverted the tropes of fantasy and mixed in post-apocalyptic themes. The coolest stuff in Dark Sun, again to me, was never mind magics, but instead the defiler/preserver duality. Psionics always felt like a way to ignore that divide and have "normal" magic. As such, it is not required for any of the major themes of Dark Sun. Instead, it's loved not because it made the setting work but because people liked the mechanics, and that's cool but not necessary to have to do Dark Sun well. The argument that's commonly made is that you need a psionics system to do Dark Sun well, and I don't think you do, at all. Dark Sun would work perfectly fine without psionics.
@iserith and
@Paul Farquhar's points about making monsters more weird is certainly a good one, but I'm not sure you need psionics to do that.