TwoSix
Everyone's literal second-favorite poster
Dark Sun is definitely a setting that could use specific, bespoke classes, rather than trying to shoehorn in everything from 5e.Mostly why I recommend a full new compatible game rather than just a setting book though is:
(a) As mentioned, third party setting books aren't exactly top sellers
(b) I feel like a setting book, especially in 5e these days, is expected to find a place for all 5e PHB player options
(c) A major selling point to Dark Sun (or a Dark Sun-alike) is that the general species are very different from what you'd expect
(d) I also think it would be a struggle to find a place for Aasimar, Dragonborn, or Tieflings, to say nothing of other options such as a classes, archetypes, or spells that don't really fit in
You would have a better standing to adopt from the OGL what you can fit in and leave things out without having to make a list of things from the PHB that are VERBOTTEN
I'm aware that Dark Sun was built from an AD&D template, but I think even the 2e version of the setting was straining against the boundaries of the existing class system.