So first, your last paragraph really does feel like some kind of post hoc reasoning - "elves should be pale and elves like the moon, ergo elves are pale because of their relationship to the moon"? I don't get the logic. (I mean, they're obviously not following or even based in any kind of biological laws here.)

But also - orcs also hate sunlight, yet have darker skin. And harfoots have darker skin but prefer the sun. (And trolls also prefer the moon, for different reasons.)

So even trying to find some thematic association within Tolkien... it's just not there.