No more Detect Good. Detect Holy instead.

[NigelWalmsley]

Better yet, not having an alignment system means you don't have to label one side being "objectively right".

The thing is, alignment doesn't mean you're "objectively right". Because there isn't an "objectively correct" answer to moral questions. It just means that the universe is on a particular side. But you're under no obligation to agree with the universe. Indeed, you very likely disagree with the universe on questions like "should I eventually die" already, without bringing alignment into it.

Basically, imagine that you can't use the words "Good" and "Evil". One side is "Purple" and the other side is "Green". Why should the output of "Detect Green" change your opinion on the morality of someone it targets?

Information density.

Alignment isn't particularly dense with information. "Chaotic Evil" includes demons, drow, Red Dragons, orcs, White Dragons, and ghouls. Those aren't really "the same" in any useful sense.

Universality.

The words "Good" and "Evil" are universal, but that's about it. Different organizations are going to have different priorities and philosophies. The Empire in Star Wars and Ruin in Mistborn are probably both "Evil" in D&D terms, but they don't have the same overall goals in any meaningful sense.

Overlaying.

It seems to me that anything you could accomplish with "alignment + traits" you could accomplish by adding an additional trait.

If you want to represent profane shrines, corrupted swamps, and so forth, there's really no substitute for a mechanical alignment system, especially in a D&D-like setting where "evil" means everything from demons to undead to aboleths so you can't just point to a handful of creatures or one kind of magic or whatever and key everything to those.

Desecrate would seem to disagree with you. That's probably the primary mechanic for representing a "profane shrine", and it doesn't make any specific reference to alignment at all. Even Unhallow only references alignment in the Magic Circle effect, which is a fairly small part of what's going on there. Not only could you have sacred sites without alignment, the existing mechanics for sacred sites largely don't use alignment. You also don't want sacred shrines to demons, undead, and aberrations to be the same thing. For example, a ghoul necromancer cult would love to profane their temple in a way that causes it to radiate negative energy, because that heals them and hurts their enemies. But people who are trying to summon demons, or sacrificing victims to an aboleth for ancient knowledge, don't want that effect.

Those "three arbitrary squares" are broad enough to contain literally the entire span of real-world moral and ethical philosophy and a broad variety of characters from fiction, mythology, and history can fit in each of those squares.

This is not helping your case. If "Good" contains "every philosophy you might hold", it is effectively meaningless. For alignment to convey useful information, it has to be narrow. Once you make it narrow, you need more than three.

Congratulations, you've just reinvented the LE and CE labels, you've just gone out of your way not to use labels because they're bad or something.

No, you've invented the "Abyss" and "Baator" labels. Those aren't "Lawful Evil" and "Chaotic Evil". Vampire Feudalism is (arguably) also Lawful Evil, but it has very different values and behaviors from Baator. The Unseelie Court is (arguably) also Chaotic Evil, but it has very different values and behaviors from the Abyss.

Hardly. The Potentium may claim that the Force is innately good and the Aing-Tii may believe that there are more shades of nuance between pure Light and pure Dark, but that doesn't mean that their views are accurate (the Potentium's "Oh, there's no such thing as the Dark Side, as long as you don't mean to kill someone with Force Lightning it's hunky dory!" stance is pretty Sith-y in outlook) or that their views contradict those of all the other Force traditions (the Aing-Tii may think the Force has "rainbow shades" but that's basically the same as saying that there are gradations of Light and Dark, and no powers they use fall outside the standard dichotomy).

That sounds exactly like "there are multiple force philosophies". Certainly, you think they all map to the Light Side/Dark Side model from the OT, but if people in-world don't think that (which they presumably don't, on account of the Aing-Tii being Aing-Tii and not Sith), forcing everything to Light Side/Dark Side isn't a useful model of the world.

Why exactly is "Acheronian" perfectly acceptable but "Lawful Evil with Lawful tendencies" an abomination that must be deleted from the game?

Consider what happens when you add a second "Lawful-Lawful Evil" philosophy to your game. If your alignments are planar or philosophical, that's easy. You just declare that there is now a new faction of people, and they have some beliefs, and maybe they have some relationships with your other factions or whatever. But if your alignments are points on a compass, you either have to do a dance of increasingly absurd subdivisions (e.g. "these new guys are Lawful-Lawful-Lawful Evil, the Acheronians are Lawful-Neutral-Lawful Evil"), or you have to do exactly the thing planar and philosophical alignment systems are already doing and rely on names to explain the differences between things.

and refuse to use labels that are applicable in settings with different cosmologies

The labels aren't applicable in different cosmologies. They're the same labels, but the Order of the Emerald Claw is not the same as Baator.

The entire Knights Radiant setup involves holy knights who gain magical powers from oaths forged with higher beings, complete with falling and losing their powers if they break said oaths, and as Kabsal said, "Everything has its opposite, Shallan. The Almighty is a force of good. To balance his goodness, the Cosmere needed the Voidbringers as his opposite," where the Voidbringers are blatant "demon-corrupted mortal" types complete with glowing red eyes and red stormlight to set them apart from the good guys who have glowing light eyes and blue stormlight.

Paladin Kaladin may not have a sheet in the back of the book that says "Lawful Good Human Fighter 5/Windrunner 3" on it, but that's still a textbook example of when an alignment system would fit perfectly with an RPG implementation of the setting.

The Stormlight Archive absolutely has an alignment system. But it doesn't have D&D's alignment system, which is the point. It's system is better in a number of ways.

First, it is explicitly opt in. There's not some weird dance where the average person is a balanced mixture of Stoneward and Skybreaker or Bondsmith and Elsecaller. They're just not aligned. That's already better than D&D's system, because it means there's room outside of the defined alignments for people who's philosophy doesn't agree with any of them.

Second, it's not claiming to be objective morality. Being a Knight Radiant doesn't make you a good guy. The Skybreakers decided to pull for Team Odium (which means there are people with glowing blue eyes on the "Evil" side too). The only Dustbringer (at least as-of the end of Oathbringer) is on Team Diagram.

Third, it's clearly defined. Kaladin doesn't swear an oath to "Do Good", he swears to "Protect Those Who Cannot Protect Themselves" and "Protect Even Those I Hate". The latter is far more useful, because we can agree what it means. Kaladin hasn't sworn himself to the abstract concept of doing things we like, he's sworn to do a particular set of things.