FYI, "Alabama Song" is in fact a Kurt Weill song from 1927, originally sung by Lotte Lenya. Morrison oversimplified the melody, arguably because he was not really able to sing it (yes, I HATE the Doors version).
yes many more could have been added for different states, like "Four dead in Ohio" by Neil Young, "Moonlight in Vermont" by various, "Massachusetts" by the Bee Gees, "Kentucky Woman" by Neil Diamond, "Mississippi Goddamn" by Nina Simone, or "Virginia Plain" by Roxy Music...