Thanks everyone for the perspectives, and please keep them coming!
As far as why I care about the obi, it's for a few reasons:
-- I store my albums stored in resealable bags, and so I'll keep the obi on the spine of the album itself, rather than under the tray. For display purposes, the albums look a lot cooler with the obi displayed than without. I care enough about this to always seek Japanese rather than non-Japanese pressings, pretty much only because of the obi. And in fact, if an album was issued without an obi to begin with, I find that disappointing
-- Most of the albums I have, I don't even need to buy the soundtrack to hear. All of the music I care about is available in native nsfe, vgm, spc, miniusf, etc. format. So if I'm buying the soundtrack, I'm buying it more as a collector than a listener. And as a collector, I want the album as it was originally issued: original discs, liner notes, jewel case, and the obi. That said, I don't go so far as to care about comment cards or external stickers.
It's not too surprising to me that albums "with obi" are so sought after. While the obi is certainly less important than the disc itself, it is a lot rarer as well (as most older albums don't include it). And for collecting, rarity definitely matters.