Agreed with the Lovecraftian influences. I don't hate Lovecraft, just peanut butter in my chocolate, so to speak.
As for aberrations, I won't say I never use any of them. I think I used a mind flayer once, in 1E and an aboleth in 2E. I don't think I've ever used a beholder. Some of the lesser aberrations -- cloakers, ropers, etc. (assuming those are even classified as such) -- don't see much use, but that's more based on opportunity than any true objection to them. For all real purposes, though, the marquee aberrations don't really exist in my home brew settings.
I do run Eberron, though, from time to time. There I don't really emphasize the Quari, but they certainly exist and I'm fine with them as part of that setting. It's just one explanation among many for things.
I shouldn't have to "cut" it from the base game. Actually, I'm fine with it being somewhere in some hypothetical 5E Manual of the Planes. I just don't want to see it baked into a bunch of other stuff. It definitely doesn't belong in anything other than a sidebar in psionics, and then only at the same level of emphasis as "and, sometimes people who have been around magical disasters manifest psionics". In other worlds, the core psionic rules should be equally usable with Dark Sun (where they come from the magical fallout) as with the Realms where (I guess) they come from the Far Realms. Neither should have to do any more tweaking to the flavor inserted into the psionics rules.
I think I agree with all this. As I mentioned in my last post, I think the art of inspiring and supporting DMs has been fading from D&D. It's a big multiverse and has room for Dark Sun with no gods, Forgotten Realms where you might bump into one at Walmart, and Eberron where the jury is out (just to pick one clear difference in settings).