Yes, bring back Greyhawk, but I'm going to disagree with you, Snarf, and call for remaining true to the Gygaxian mold (and take "mold" in whatever way you want).
My protest is one of aesthetic principle, and really extends towards a wide range of media. Too often old things are remade and painted over, and lose their original, archetypal form and quality. There is something to the idea of riffing within a limited set of parameters; just as jazz or raga players solo within a theme of musical phrases and qualities - it isn't just chaos.
This is why I think, in some ways, Golarion is a more cohesive setting than the Realms: it was designed with being a shared world, and to continually be expanded upon. It may have started as Erik Mona's , but it quickly become not just his (TBH, I don't know anything about its origins - and it may be that its coherency is due to his oversight? I don't know).
The Realms, on the other hand, had existed for two decades, in some form or fashion, before the publication of the gray box. And Greyhawk was distinctly Gygax's until he was exiled from the realm.
This is not to say that I think post-gray box Realms is bad, or even that post-Gygax Greyhawk isn't truly Greyhawkian. But even the best longbows--if bent far enough--will break. At the least, FR became more and more "heapish," and lost some of is distinct Greenwoodian flavor.
I mean, let's face it: Al-Qadim is cool (and, quite frankly, cooler than Calimshan), but does it really make sense in the Realms? And is it necessary, with Calimshan? And don't get me started on Maztica or Kara-Tur, not to mention the Horde and Moonshaes.
Now this is not to say that you're suggesting that they "Realmsify" Greyhawk, but that adapting or updating it into a different cultural milieu can end up diminish its signature quality.
It is a similar aesthetic issue I have with updating other media to the current context: it often feels rather cheap and, dare I say, colonial and is sometimes (though not always) ideologically motivated - like the new creators want to erase the original vision and put their own stamp on it. Some things can be revisioned; I liked both the Nolan Batman films and was pleasantly surprised with the new one that just came out, even though I still have a special place in my heart for the Tim Burton/Michael Keaton one (and yes, I know there are earlier forms of Batman). But in both cases, they worked because the revisioning played within certain themes; and the changes were aesthetic, not ideological.
There is another option: Why not, instead, create new worlds, new superheroes, new ideas that are created to express the ideas you want to explore? Why not create a new D&D setting, even a kitchen sink one, that can be endlessly expanded upon? A Golarion for 5E?
In other words, I don't think dragonborn (or whatever) belong in Greyhawk, and I think Greyhawk is lesser for having them. I mean, why are they necessary at all? Certainly, individual DMs can do what they want and cater (or not) to the desires of their players. But as far as the published books? Keep the aesthetic signature that is unique to Greyhawk. Otherwise, yes, it feels closer to the Realms or just any generic branded D&D world. What ends up happening is a diminishing effect. Chris Pine is a solid actor, but he's not Kirk. William Shatner is Kirk (in the case of Star Trek, I would have rather seen an entirely new space franchise, or at least a different captain and era - which is why Picard and TNG was great...it was still "Star Trekkian," but wasn't painting over the original).
The settings are an opportunity to explore different themes, to combine different elements of D&D lore in unique ways. We don't need starshimmer elves in Dark Sun (or whatever), and we don't need nice drow in Greyhawk. Let the worlds be distinct. D&D can be many things to many people - that is a strength of the game that can and should be exploited. But if everything becomes only some things to some people, it lessens its potentiality; or if everything must be included in some form or fashion, not matter how it jars with the aesthetic signature, it diminishes distinctiveness.
