Aside from the reminder about the whole "all the worlds in a single multiverse" bit, Wyatt starts things out on a pretty positive note.
He opens with 3rd Edition's Manual of the Planes. Yeah, it mapped out the Great Wheel, but also had entire chapters dedicated to helping you design your own cosmology and explaining each plane individually, so if you felt the need to adhere to various Dungeons & Dragons quirks--such as spells that require access to one of the transitive planes--you knew what you were getting into. Finally, it gave you five examples to work with.
He then moves on to 3rd Edition's Deities and Demigods, which included cosmologies for the Greek, Egyptian, and Norse mythologies, the World Tree cosmology from 3rd Edition's Forgotten Realms, whatever you would call Eberron's cosmology (I guess the Orrery-riff), and the "default 4th Edition cosmology" formerly known as the World Axis.
Really the first half of the article speaks to the strengths of 3rd Edition's approach: you give Dungeon Masters the tools and knowledge to construct exactly the cosmology they want. Though I found the World Axis much more engaging and useful as a default, and the lack of strange rules interactions made it easier to build your own without having to worry too much, it still kind of sucks that 4th Edition never saw the same treatment. It seems like 5th Edition will not either--or, at least not as much--because apparently there are "pitfalls".
The greatest of these pitfalls, according to Wyatt, is "eroding" the intellectual property of Dungeons & Dragons that "everyone knows about", like where demons come from and the Blood War.
Frankly I doubt that most gamers are aware that demons come from the Abyss. They are probably at best aware that they come from a generally "bad other world", and if you gave them a list of planes they might ironically pick the Nine Hells, because demons coming from hell sounds logical. I would wager that even less are aware of anything pertaining to the Blood War besides its name.
On that note, is the Blood War "an important element" of Dungeons & Dragons? Even though I played a lot of Planescape I never used it, and I do not recall it being relevant in any other setting or the focus of an adventure. So besides it being an older bit of esoteric lore, why is it so important? Or is that the only criteria that matters?
As for how you would shoehorn the Blood War into Eberron or the 4th Edition cosmology that shall not be named (which would be incredibly easy), the obvious answer is that you would not, just like you did not in, say, Dark Sun. Honestly it is not important or necessary that demons come from the Abyss (or even another plane), or that the Blood War is a thing that exists despite most groups never interacting with it in any way. These so-called pitfalls are in actuality non-issues.
The best approach would be to just present the elements as setting-neutral, and then put any relevant changes to the defaults in a setting book, kind of how they did it with 2nd Edition's Dark Sun. The default game does not need a Great Wheel or Blood War: both can be reserved for Planescape, or possibly another setting that actually uses them. Demons in Eberron can come from another plane, possibly two, and in yet another setting that might be native to the mortal realm. That sounds a lot more conducive to creativity and flexibility than kind-of-sort-of maybe homogenizing everything for the sake of tradition.
So unsurprisingly they are going with the Great Wheel as a default (tradition and all). 3rd Edition clearly proved that you can give Dungeon Masters the pieces and let them figure it out without "eroding" the game or whatever. Wyatt will apparently talk about other options, so maybe he will elaborate on how well 5th Edition will support different cosmologies, namely Eberron's and [4th Edition cosmology].