If I was king of the world this is what I would do. Each setting would have a distinct cosmology. After all, if I'm playing Greyhawk or FR or whatever, then presumably I like that setting.
So why should I give up that setting as soon as I go planar? FR has a boat load of active gods. Does it really need Orcus, say, and how does Orcus fit? So maybe FR abyss doesn't have Orcus. Otoh, Greyhawk certainly does need Orcus.
But the Abyss of FR and the Abyss of Greyhawk don't need to share anything.
I'd then have a Planescape line that is additive. If you go from Prime X to
Planescape, this is how you do it.
To me, that's the best of both worlds.
Your logic is sound, but I can't shake the feeling that if separate cosmologies have place names in common, those place names should refer to the same place, just for the sake of clarity. There's no /need/ for separate Torilian and Oeridian Abysses.
The realms of St. Cuthbert and Torm both exist in the Seven Heavens*, but they are unrelated and have little to no interaction, because why would they? Torm has no followers on Oerth and St. Cuthbert has no followers on Toril**. But if PCs want to make the trek across the snow-capped peaks of the soul, you can get there from here. It's just a tough climb.
When you visit the Seven Heavens from Oerth, you are visiting the realms of St. Cuthbert and the other LG gods of Oerth. They are interesting and new in their own right, while still being familiar, and provide additional adventuring options for Greyhawk PCs without the involvement of irrelevant material. Likewise for Toril and Torm's realm.
Then, Planescape's patented brand of weird is what
fills the gaps. With no regular connection to any prime material world, the interstitial spaces of the planes have gone native, and that's what makes inter-prime travel fascinating. The lands you have to pass through are unlike anything you've seen.
Unique planes can still be unique. Khyber, Cynosure, and the Grey have no Oeridian equivalents. They can only be reached from Eberron, Toril, and Athas, respectively, and that's fine. There's no need to shoehorn them into similar places from another cosmology. They have different names; they're different places.
...So, in short, I agree completely except for where I totally disagree with you. It just seems to me that if there's an Abyss in D&D it ought to always be the same Abyss. The Krynnish Abyss might be an exception to this rule, or maybe it's not. Maybe there's a good story reason why Tiamat spends time in the Abyss calling herself Takhisis.
*I forgot Mount Celestia was a Planescape thing!
**There must be some rule about evangelizing on other gods' turf. And it must be a complex rule, because it doesn't stop FR from having a dozen or so Terran gods.
