This does beg the question: if a setting requires major revision to the 5e game mechanics to run (so much so that whole races and classes must be rewritten) than is there any advantage to running it in 5e rather than running it in its original edition?
Yes. The mechanics of 5E work much better than the mechanics of 2E.
To do Dark Sun well in 5E, you need to do what they did when Dark Sun was first released: Build a specialized campaign setting. If you really like the vision, it is worth the effort.
I would:
1.) Eliminate the cleric and paladin classes.
2.) Add a Templar class that is similar to the cleric, but designed to fit the theme.
3.) Create 2 psionics class (Psion and Psionic Warrior). I would also create a few additional subclasses, including a Sorcerer King Warlock Pact, a Preserver Wizard, and an Elemental Druid.
4.) Add the Dark Sun specific races.
5.) Add a resource tracking system that expands rules for dehydration, starvation and exposure. These are essential elements of Dark Sun and this is the only setting where I would even tolerate, much less recommend, them.
6.) Add defiling as the default when using magic, and create restrictions on magic when someone preserves.
7.) Rewrite the entire history of Athas to introduce new storylines, Sorcerer Kings, etc... The old materials were so 'railroad' that anyone that is a fan of the setting knows too much.
I'd also use the old monster books to add abilities to existing monsters to give me Dark Sun threats.