Eberron's core philosophy is that if its in D&D, its in Eberron, so Eberron will follow suit.
This was markedly not true of Eberron's cosmology during 3e. I'm not sure whether it'd pick up the 4e cosmology or not, since all of the Eberron planes are basically reskinned planes of the old cosmology, but the Far Realm and the Plane of Dreams are the main planes of importance (or, uh, bad guys, at least) in Eberron's cosmology - not the Abyss or the Nine Hells. So, essentially Eberron wouldn't necessarily be
hurt by adopting the 4e cosmology but it
would be hurt by adopting ideas like "at epic levels you go to the Abyss or the Nine Hells or other Astral Dominions and punch out bad dudes".
Athas was very focused away from other planes, so I'm curious to see where that goes.
I haven't read my Dark Sun books in a long time but I think the biggest "problems" with it using the 4e cosmology would be the Feywild and Shadowfell - it generally was just 100% about the world, so people who regularly wander through a different plane to travel 20 feet would be kinda out of theme. The Elemental Chaos and Astral Sea can exist and it'll just be that no one cares. (Also, the Fey
wild is kind of out of theme as coterminous with Athas, though it could be played up as a vision of Athas as it was before Bad Stuff Happened...)
Krynn's cosmology was half-assed and lame, and won't be missed, at least not by me.
It's pretty generic D&D, so far as I recall. The one cool thing I remember is that the gods were visually represented as constellations. We can surely keep that. (Though it makes Star Pact Warlocks kinda funny.)
Oerth, I've never been familiar with.
Used Great Wheel by the book. Much like FR, wouldn't really be hurt one whit by transferring over to the 4e cosmology. They'd probably massacre the setting and kill off all the gods and that will hurt it, but that's not a cosmology issue.