Now I do find it baffling why 4e didn't just narrow it to good, evil and unaligned since leaving in remnants of Law and Chaos attached to good and evil respectively isn't really true to any source and heavily prejudices what those cosmological forces represent. It's basically making Law equivalent to good and Chaos equivalent to evil (a simplistic and incorrect view at best which really mudies the waters for those who want their major cosmological conflict to be based around those forces)... or better yet just eliminate alignment all together and let DM's decide on their own cosmological forces in game. I could have got behind them saying hey we want the default to be games of good and evil not chaos and law but instead they did a half-hearted removal which in my opinion kind of missed the point on both fronts.
I would have been fantastic if WotC had gone with a set of possible alignments.
As to why they did 4E's alignment system as they did, there were likely a number of factors at play here. By no means, am I suggesting that my explanation is exhaustive or definitive. QuietBrowser touched upon one of the issues, namely
Alignments in Theory vs. Alignments in Play. LG and CE are probably the most easily grasped alignments, however superficially, by casual people. It's not hard to grasp the fundamental philosophic difference between Law, Order, and Goodness on the one hand and Chaos, Destruction, and Evil on the other. LE and CG represent two other common tropes, particularly when played against each other: Evil Tyrannical Oppressor vs. Good Liberator for Freedom! But part of the problem rests not so much in these four extreme points, but in the in-between and how these relate to the extremes. Chaotic Neutral is probably one of the most reviled alignments in D&D. From my own experience, I would much rather a PC be Chaotic Evil than have to deal with a character with the Chaotic Neutral alignment. Namely, because often a player uses the CN for their character to be evil
de facto without being evil
de jure. Chaotic Neutral in theory is about freedom and "Chaos" without regard to good or evil. The problem is that in-practice, CN usually veers towards Chaotic Evil or "unaligned" (as per 4E). That was also likely a similar reason for the synthesis of Lawful Evil and Neutral Evil. In-practice, these alignments are frequently played, on the whole, as "non-destructive/chaotic evil," which 4E simplified to "Evil." Same thing again for Chaotic Good and Neutral Good, albeit with these alignments frequently played in terms of their relation to Lawful Good: i.e. "good that's willing to operate outside of law/order." Hence the reduction to "Good."
My second suspicion is that WotC wanted an alignment system that more closely mirrored their meta-narrative's
aesthetic. Not so much the meta-narrative itself, but the
aesthetic. Again, QuietBrowser astutely mentioned the presence of the
Chaoskampf motif in 4E's cosmology. The aesthetic of 4E's cosmology is mythical. It harkens to a lot of ancient myths of human civilizations (e.g. Canaanite, Assyrian, Greco-Roman, Germanic, etc.). "Order" has a positive cultural association while "Chaos" has a negative cultural association that approximate moral senses of good and evil. Good actions uphold the cosmological order, while evil actions pervert order, thereby threatening the return to chaos, lawlessness, and barbarism. Although the 4E gods are of various alignments, there is a general sense that the gods are aligned with "Order" while the Primordials/Titans are aligned with "Chaos." When you compare the ethical system in the mythical aesthetic that I mentioned with the 4E alignment system, it's not difficult to see the philosophic overlap.
In some respects, 4E's alignment probably more closely mirrors my sense of "mythic alignment" as well as how these alignments often played in-practice, so I cannot discount personal biases in my two explanations above. But as I said before, I am a fan of Law vs. Chaos. So when I see the 4E alignment system, I don't necessarily think that it reflects a cosmological "reality," but, instead, that it reflects humans (and other mortals) imposing their own moral sensibilities on the (Law/Chaos) cosmology. In other words, the 4E alignment is reflective of the normative moral/ethical perspective of the human subject.
As something of an aside, though related to being a fan of Law vs. Chaos, I feel that I am one of the relatively few people below the age of 35 who have read Moorcock's Eternal Champions. You may know others, including yourself, who have read them, but I have not met many people who are familiar with these books and much less those who have actually read them. You can just about tell someone's age when they think that a soul-sucking sword is a rip-off of Arthas the Lich King's Frostmourne in WoW and not of Elric of Melniboné's Stormbringer.