I don't know about you, but it took me a long time to get here. I actually used to think of D&D (back in the '80s) as something like a setting-agnostic system. It's only after digging into those early books with fresh eyes after many years that I came to realize that the game Arneson and Gygax created is set in a world where all their influences from swords and sorcery and medieval high fantasy are in play. So Alignment isn't a way of understanding characters from fiction that was put in to help players role-play. It's part of the setting of D&D which is a place where Moorcockian Law and Chaos are really at odds with one another. That's why I use alignment in my D&D games, because when I play D&D, I want to play that game. I want to play the most D&D version of D&D I can play.
My pathway was different.
Like you, I used to think of D&D (back in the 80s) as a setting-agnostic system. After reading an excellent article in Dragon 101 called "For King and Country" which through both abstract argument and a worked example showed how alignment makes a mockery of a whole range of standard settings, I took up its advice and dropped alignment from my FRPGing.
For nearly 20 years from 1990 my FRPG of choice was Rolemaster - which presents itself as, and which I mostly treated as, setting-agnostic. We never used alignment in our RM games, although from time-to-time would engage in the pastime of imputing alignment descriptors to the various PCs who passed through that game (Penn was CN; Xanthos was LE; Xialath was probably NE; Luvian and Tabernacle were perhaps NG; etc). I used D&D settings for those RM games - the World of Greyhawk for one, and Kara Tur for another. The GH material worked fine shorn of alignment - St Cuthbert works as an object of religious veneration by simple peasantry and townsfolk without needing the LG(N) label; Hextor is a six-armed destructive force who is implacably opposed to Heironeous without needing the LE label; etc. The Kara Tur/OA material likewise worked fine shorn of alignment - we had gods and spirits and dragons and constables of Hell and lords of the animal kingdoms and the like, and the various intricate relationships between them, without needing to give them alignment labels.
When I started a 4e D&D campaign in 2009 the players stuck alignment labels on their PCs as the rules told them too. I wrote alignment labels on my NPCs and creatures as the rules told
me to. The player-side labels I left to the players to worry about: four were unaligned (a paladin of the Raven Queen; a cleric/ranger serving the Raven Queen; an invoker/wizard serving a variety of gods including the Raven Queen, Ioun, Pelor, Bane and Vecna; a drow sorcerer/bard devoted to Corellon Lorethian and that Elven gods one-time ally Chan, Queen of Good Air Elementals); one was good (a cleric/fighter of Moradin who ended up taking Torog's place as god of imprisonment and punishment). It was those other allegiances that really drove the campaign - eg the invoker/wizard and the drow sorcerer would frequently clash over law/civilisation vs chaos. The alignment labels served as loose personality descriptors that also played a role (a secondary one) in locating the PCs within the cosmological context that their more particular affiliations also related to.
As a GM, I used the labels that were on my NPCs/creatures to make sense of their cosmological orientation and as loose personality descriptors in the way discussed in this thread. I think the game would not have lost anything had they not been there - when I read that Orcs are destructively-inclined worshippers of Gruumsh it doesn't really tell me anything further to label them CE - but they were harmless enough. I felt the game overall had a strong law vs chaos feel to it (but not quite Morcockian because not grim enough) but the alignment labels were probably following rather than leading in this respect.
