In cases like “The The” or, let’s pretend there’s a band called “The” (and for all I know, there may be one), that would of course get alphabetized under “The, The” and “The.” There’s no confusions there, because where else in the alphabet would you look for a band named “The”? I figure leaving off “the” and other articles when alphabetizing is to keep things simple. How many people remember whether it’s “The Pixies” or “Pixies” (it’s “Pixies” on their albums). Is it “Beatles” or “The Beatles”? (“The Beatles.”) Or you’d have the stupid case where some Smashing Pumpkins albums are under “The Smashing Pumpkins” while others are under “Smashing Pumpkins.” Eliminating the article makes it easier to find. You don’t have to potentially look in two locations in the index trying to figure out if the indexer filed it under the article or not, and you don’t have to remember whether the article is officially part of the name or not. With a name like “The” or “The The,” it’s pretty clear you have to look under “T” because where else would you look? Plus, in the first case, I’d argue that “The” isn’t being used as a definite article, anyway, it’s a proper noun, and in the second case, I’d say the first “the” is an article, but the second one is being used as a noun.