I don’t think there’s an obsession with turkey: It’s just traditional to serve it on Thanksgiving. For many of us, it’s the only day of the year that we eat it, except for leftovers. If there is an “obsession”, I’d say it’s more of an obsession with tradition. Thanksgiving, being in Autumn, lends itself well to a set menu, with “fall-ish” kinds of things, so this holiday is the one, for most of us, with a fairly “set” menu.
It’s generally one where the main components complement each other well, with the tart, tangy, cranberry sauce offsetting the rich gravy and dressing, etc. I look forward to it every year, never to repeat it during the rest of the year.
It’s a tradition, even in its regional and familial variations, that brings a country full of disparate people together, if only for a few days: We’re all madly grocery shopping, comparing notes on the best way to get the dark meat done at the same time the white meat is; gravy with giblets or without (there’s always someone at every gathering who likes it with and someone who likes it without) and the southerners who’ve never had pumpkin pie (and likely never will) vs. the northerners who’ve never had sweet potato. (But whether pumpkin or sweet potato, most agree that one of the two is an integral part of a Thanksgiving dessert table.)
It’s a tiny slice of commonality in a vastly diverse nation. I find it delightful!