FR and GH are the very definition of generic high fantasy, and are just canvasses that you can easily mix and match and alter without any big deal.
FR I don't pretend to understand.
But GH I think I have a bit of a handle on: I think I own and have read most GH RPG supplements that have been published, and I've been running games set in GH for around half of the past 30-odd years.
I see GH as a version of the Hyborian Age: it gives us pseudo-historical locations all good-to-go for fantasy action adventure. It has ancient and magical cultures (esp the Suel) to be a source of Xaltotun and Thugra Khotan types. It has knights if we want them (Furyondy for feudal; Nyrond for somewhat more Byzantine). It has cities of thieves (eg GH, Hardby, Highport) which can contain as many Towers of the Elephant as a campaign requires. And, unlike REH's Hyborian age, it also has lots of Tolkienesque elves, dwarves etc, and even some handy forests (Suss Forest, Gnarley Forest) for our rangers (Aragorn, Sons of Elrond, etc) to do some serious orc-fighting in!
The middle of the map even puts all of these things within a handy 10 hex radius, or thereabouts, of Hardby: the Bright Desert for mysterious ruins and ancient Suel tribesmen; the Abor-Alz for hill tribes and badlands along the lines of People of the Black Circile; the Nyr Dyv and the Wooly Bay for saiing and pirates; numerous cities and towns of slighlty different flavour (the Leiber-style GH; Dyvers; Verbobonc; Hardby; Highport with its slavers; etc); the elves of Celene with its forest borderlands, the dwarves of the Lortmils and Kron Hills, and the orcs of the Pomarj and Wild Coast; etc.
There is stuff that doesn't really fit well with this world (eg a Sauron-style unified evil threat; if you want that it's Furyondy vs Iuz rather than the whole of the Free Peoples vs Sauron). But there is a heap of stuff that does fit with it: ruins, thieves, intrigue, ancient wizards/liches and the like; cults; etc.
And (not to beat too hard on a dead horse) I think a mysterious order of lunar wizards is not out of place. No snake cults and their temples. Nor grim barbarians of the north who worship doom-ful gods like Crom, or Kos from the Newhon chapter of DDG.
Give tnat GH is a pastiche of a pastiche, and deliberately so in order to support FRPGing, the idea that a GM treating it as such and adding to the pastiche is somehow
mistreating the setting makes no sense to me at all. In fact, it verges on contradiction!