Once I was at home, and the thought reoccurred to me, I further thought that surely someone must have already done that. A quick google confirmed that yes, lots of people have. Here are four, all from the first page of google hits: the Guardian, Esquire (the most annoying web format by several orders of magnitude), some site called 'buzzsugar' and a blog with the charming title of 'ipickmynose'. (Note: for the rest of this post, as a default, I'll give all lists in that same order.) They're not all strict about the song title element, but they're clearly all variations on that idea.
It's interesting to see what gets chosen. One (buzzsugar) chose the Dar Williams song for its Iowa selection; another (ipickmynose) made it a runner up. (Esquire and ipickmynose listed runners-up; the other two didn't.) The other three chose Joni Mitchell's "The Dry Cleaner From Des Moines"*, Canon Blue's "Indian Summer (Des Moines)" and Eleni Mandell's "Iowa City". All four -- yes, all four -- chose Bruce Springsteen's "Nebraska", which was one of my first other thoughts. (As Esquire says, "sometimes song selection comes down to Occam's razor — the obvious song is the right song".) None of them chose yet another early thought I had, Nina Simone's "Mississippi Goddam" for Mississippi -- but I suppose I can see why they didn't.**
Three of the four chose Camper Van Beethoven's "History of Utah" for Utah; the exception was Esquire, which chose The Grateful Dead's "Friend of the Devil", explaining "sometime a passing reference is as good as it gets. At least we weren't forced to pick an instrumental." Two (Guardian and buzzsugar) picked Lynrd Skynrd's "Sweet Home Alabama" for Alabama; Esquire gives it runner-up status, picking Jason Isbell & The 400 Unit's "Alabama Pines" for first place; ipickmynose overtly lists it as "not considered", giving pride of place to the Drive By Truckers's "The Boys from Alabama" and listing a lot of second choices too. Buzzsugar actually gave 51 choices, picking The Postal Service's "The District Sleeps Alone Tonight" for Washington D.C.; ipickmynose went them one better, and gave not only a D.C. choice (which was the same song by The Postal Service), but also gave choices for Puerto Rico (Pepe y Flora's "Puerto Rico Tiene Minas") and, rather cheekily, Canada (Low's "Canada")***, as well as listing (as a "theme song") Sufjan Stevens's "50 States Song". (ipickmynose -- God, what a name! -- also gives links to mp3's, if you're interested.)
Anyway, click through and explore if you're
* After a brief error about the location of Kalamazoo (Michigan). Cut them some slack, they're British.
** Robert Johnson, "Cross Road Blues"; Hank Williams III's "Mississippi Mud"; Sugarland's "Down in Mississippi (Up to No Good)"; Waylon Jennings's "Mississippi Woman".
*** Way back in '96, I saw in The Onion -- on actual dead-trees paper, which was how most of us read the Onion in those days (he said, shaking his cane at the kids on his lawn) -- a story headlined "Perky 'Canada' Has Own Government, Laws."**** I thought it was hilarious and showed it to a lot of people, both Americans and Canadians. All the Americans thought it was hilarious. The Canadians didn't, but rather than offended, they were puzzled: well, of course we do. What's funny about that?
**** Oddly, until googling this just now I remembered it as "Perky Canada Has Own Laws, Borders." I would have bet serious money on it. As Nabokov says, "Mnemosyne, one must admit, has shown herself to be a very careless girl". (Except until looking it up to quote it I remembered it as "unreliable" instead of "careless".)