I think I realized why Sauron works as a villain, at least for me.
Sauron is often seen as the prototypical example of the Dark Lord, the excruciatingly boring stock villain of classic high fantasy. He’s the dark component of a reductive black-and-white morality. He sits in a tower and wants to conquer and/or destroy everything. His tools, his servants, his lands are all foul, ugly, barren and evil. No real motivation, no personality to speak of. (Especially in contrast to the secondary villains and anti-villains in LOTR, who all have their stories and all but overflow with personality.)
Real Tolkien buffs, the ones who are buffer than me, will tell you that Sauron has an incredibly complex backstory, mostly contained in the Silmarillion, with bits and pieces all over Tolkien’s writings. Sauron has led a long and complicated life, going by various names and identities, serving evils greater than himself, getting destroyed but surviving multiple times, doing evil, repenting, faking repentance, doing evil again, going native in various ancient civilizations then contributing to their destruction, etc. If you read all the supplementary material, piece it together and fill the gaps with your imagination, Sauron is a noble, interesting, complex villain.
Very little of that comes through in LOTR itself, but I think it doesn’t need to. I think Sauron functions as a fantastic villain in LOTR exactly because we know so very little about him. Sauron has no POV chapter, except for a few paragraphs, and no POV characters ever encounter Sauron in a direct and comprehensible way. He mostly acts through proxy, his captains make war for him, his proxies speak for him. The reader never feels that his characterization is insufficient, because he *has no characterization*, he’s too far away and too high up, unknowable. Mostly Sauron is spoken of in the abstract, as the ‘enemy’, as the cause of evil, not as a specific evil person to be defeated. After all, it’s pretty clear he cannot be defeated, not in person. And when someone has a real and somewhat more direct encounter with Sauron, either via a palantír or in a vision, Sauron is too powerful to register as an individual person: he is an eye, a flame, a force, a will, a seeking attention. He is too big and too close to see as a whole, he is in your head, intruding, terrible.
So the narrative places Sauron in a context where he is either a distant menace, or an immense, incomprehensible mindfuck. Although he feels emotions such as wrath or fear, and he makes cunning stratagems, he doesn’t read as a strong clever evil person, he mostly reads as a force, as sheer power that only seeks more power. And on the whole, I feel that he *is* just that: not a person, but a power-hunger itself. It is stated in text that he’s a diminished, weakened, wounded version of himself, that during his different attempts (and failures) to subjugate others, he kept losing parts of himself, first his ability to assume a pleasing form, then to embody himself at all. I get the implication that he used to be a complicated entire whole person, and his struggle for power slowly eroded him, sanding off quirks and traits and individuality, costing him his patience for beautiful craft and his interest in beautiful languages, until he could no longer even pretend to be a fellow-person and not a *power*. Until he became an creature made of, and by, his own power. He was a person but power ate him and now he’s gone: this is the threat and the lure of the ring, which Sauron made of, and for, himself. Interactions with the ring are the closest thing we come to genuine interactions with Sauron, or to insights into Sauron’s mind – and interactions with the ring are uniformly horrifying, except maybe the one time Sam is small enough and kind enough to laugh it off. And seeing that, it’s clear that the ring needs to be destroyed, and Sauron’s power needs to be destroyed, for Sauron’s sake too. Only when he’s cut off from his power can his lost houseless spirit find its way through, to redemption or even just to rest.
TLDR: I don’t usually dislike villains who seem to seek power for power’s sake, but Sauron feels like a fantastic deconstruction of that: after all, LOTR is mostly about the risk of individual people becoming corrupted by power and becoming the vehicle of mere power-seeking-power-for-power’s-sake, and Sauron is someone to whom that already happened.