A few of your assumptions are a bit incorrect, but to be honest, they're close enough. Others have mentioned a few, and I started writing my own corrections, but it all came out being a bit petty.
So, the big advantage to Greyhawk is that it's the easiest drop and play published setting, save for perhaps Mystara. Depending on the amount of information you want, you can pick up a book or two and get started. The two best sources would be the 1983 Boxed Set (1E) and the Living Greyhawk Gazetteer (3E), but the From the Ashes boxed set (2E) could be used depending on the kind of game you want to run. All of them pretty much provide an amount of information for the setting, with varying degrees of details (later editions are more detailed). The information is enough to give the DM ideas, but limited enough for the DM to fill in with their own ideas. It is the perfect balance between the work of making your own setting and the constrictions many other published settings place on the DM with existing canon.
The other huge advantage that Greyhawk has is the variety of regions for adventure. A Game of Thrones style game can be easily placed in the Great Kingdom (an empire crumbling in on itself). Vikings live in the far northeast, with 4 semi-allied factions. A game about defending the free people against a tyranical empire can be done in Nyrond and the Iron League holding off the Great Kingdom. Urban intrigue, with a massive sewer system can be found in the Free City of Greyhawk. A game about knights facing the forces of an evil god can be found in Furyondy, the Shield Lands, and Velona agains the Empire of Iuz. Political and economic rivalries between good nations can be found between the Nations of Furyondy and Nyrond. the Bright Desert and the Vast Swamp can provide adventure in harsh enviroments, as can the jungles of Armedo and Hepmonaland with its Incan-like savages. The Baklunish basin in the northwest provide arabian adventures, while the Wolf and Tiger Nomads provide barbarian culture adventure. Blackmoor, the Land of Black Ice, and the legendary City of the Gods to the far north provide arctic adventures, spiced with the strange. Piracy can be found from the Sea Barons and the Sea Princes. Pretty much every type of adventure and campaign can be found in the Flanaess (the area Greyhawk focuses on) EXCEPT for oriental adventures, which was originally worked on by Gygax, but never officially installed (Kara Tur was originally supposed to be on the other side of the world from the Flanaess, but TSR moved it to Realms instead).
If I had to put an actual downside to Greyhawk, it's the deities. In no edition do they do a sufficient job explaining why there are so many overlapping gods, nor explain the hodgepodge pantheon system laid out. If having clear religions is a big deal for you, this can be an issue.