See the horrors of Ithaqua? Of Cthulhu's Siren Song? Those are your brethren turned mad. That is your potential fate.
See the Mi-Go? That is what some of your people in the Silver Legion made of humanity to make them 'Better' in the war. Of course, now they have been contacted by the Things Beyond many of them have warped further still. What of the Deep Ones? Well, Belial (now Cthulhu) needed a hobby and through dreams and lore they were carved of mortals who walked into the waters well after the Earthbound were re-summoned to Earth.
In this version, however, the Fallen didn't make the universe but the galaxy and God is an entity that sits within the sun. It consumes sentient thoughts, hope and faith, having been gutted by its brushes with the Things Beyond and having heard the tunes of the Court of Azathoth since the Fallen rose humanity to sentience and thus shook the foundations of reality itself. God never smote the world in revenge against the Fallen. It never cursed them out of spite. Oh no, it simply offered the only real way to keep reality in check. And when humanity became sentient, reality cracked as the slithering tendrils of the Things Beyond began to roam. Knowledge is a potentially deadly and corruptive force in the Lovecraftian worlds, after all.
Thus, everything the Fallen ever believed in is a Lie. They live in a crumbling reality filled with an essential decay which has snaked into their brethren (the Fallen) and slowly warped them in horrifying and maddening ways. Of course there could be some Great Horror with what God was doing with human souls, perhaps using them to shore up reality itself, but to be honest it's more horrifying if God was simply a compassionless figure who couldn't understand reality but wished to create a place to slumber.
Then Second World spoken of for the Slayers which was slowly being built by the dead spiritual matter of plants and animals could well become the holding place for human souls, lacking a better option, since humanity contains a spark of the Thing in the Centre of the Sun but were too contaminated by reality to rejoin with it. Perhaps? I'm not sure what to do with that.
Naturally Azathoth, Shub-Niggurath and Yog-Sothoth would remain essential principles within the universe rather than sentient entities in their own right because it's simply cooler that way.
And yes, it definitely changes the feeling of Call of Cthulhu, but having allowed my players to become supernatural does that on its own. So why do it? Well, I love Demon: the Fallen characters but I love the Call of Cthulhu campaigns and while it changes the setting immensely and the style of horror invoked it doesn't change that these campaigns will still be good and fitting for what I want to do.