I'm not terribly swayed by the cosmology argument, because you could keep those arrangements without explicitly mapping them onto the personalities of everyday randos here on the material plane.

In fact, "good" and "evil" in a character's alignment already doesn't really mean the same thing as "good" and "evil" in the sense of Elysium vs Hades. You could easily swap "Good" with "Celestial" and "Evil" with "Fiendish" without changing anything at all about the cosmology.

In the end, I think that the classic D&D alignment structure is not currently useful for defining player characters, and is only slightly useful for describing mundane foes. It doesn't really map to any real-life philosophy of people generally, and more importantly, it doesn't map well to modern fantasy storytelling and characterization.

For a different example, consider Magic: the Gathering's color pie. This approach also doesn't really map to any real-life philosophy of people, but it's excellent at dividing the world into narratively compelling philosophies. It's very customized to its purpose as part of a trading card game, though—it's interesting to describe the colors of fictional characters, but it's clumsy when you try to use it for PCs. You'll notice that even the Planeshift materials that bring M:tG content into D&D largely drop the concept of color.

So what is useful for PC characterization? I agree with GreatWyrmGold here: It's things like Personality, Traits, Bonds, and Flaws. These are the things that make my characters very different from each other, regardless of their alignments or their "color".

Bringing these explicitly into character creation is one of the best moves 5e made, IMO.

(So my final answer to the OP's question is: D&D does not need alignment for PCs or most enemies. It still has a place in the cosmology, and for creatures associated with the Outer Planes in some way.)