I don't see an issue with not calling it psionics and just having it be something else. Or just dropping it entirely and having magic in general be much more rare. Going lower magic in a setting predicated on gritty survival doesn't seem problematic to me.
I agree that Preserving and Defiling are fundamental to the setting, but I'm starting to wonder if having an alternative way of gaining powerful magical effects actually backgrounds the ecological trope more than is necessary. If there is no other way to do magic, that makes the Veiled Alliance's efforts to maintain humane magic all the more heroic.
I don't think it's "problematic", I just don't think it leaves you with something that's even particularly close to Dark Sun.
The Veiled Alliance as is doesn't even make sense without psionics being out there as the main, day-to-day form of magic, really. Without psionics to like "get in the middle", and to be the dominant form of day-to-day magic, the shape of the setting would be very different. The battle lines more clearly drawn. The Veiled Alliance would be vastly more powerful and harder to hide, and they'd be even more in-demand.
The Elemental Priests and Druids would also be significantly more in-demand, and likely significantly more powerful. It makes far less sense for them to be these weird outsiders only, if there's no psionics. So you'd expect them to be more powerful and organised, and likely inside the cities, much as the Templars might not like it.
Templars would have a harder task dealing with Preservers and Defilers, and with trying to keep out the followers of Elemental Priests and so on.
People's day-to-day lives are very different when they can't all call upon minor psionic abilities. Even if you replace that with physical mutations (as you suggest) you end up with a rather different vibe (one that is somehow "more '90s" I'd say, weirdly enough).
I'm not saying it wouldn't be "cool", but it would be a pretty drastic re-envisioning of Dark Sun and would be missing a lot of the heart of Dark Sun. I think the FR with the god having suddenly an inexplicably vanished would be a cool setting, but I just wouldn't say "This is the FR", but yeah "alt-FR" or something. Except not that because people might think you mean "alternative far right"... so er um, "Modified FR" I guess.