She might not have an "obvious" song or album that folks automatically associate with her
but I see that as more of a result of her cult status than the cause. As far as fans are concerned, '64's "In Concert" seems to be the most highly regarded album, partly due to the inclusion of "Mississippi Goddamn" which is her most infamous song. "I Put A Spell On You" (both her version of the song and the accompanying album) seem to be fan favorites as well. Additionally, both "Feelin' Good" and "My Baby Just Cares For Me" have recently been used in high-profile ad campaigns. And Kanye sampling her version of "Strange Fruit" probably got that one some attention as well.
I still get what you're saying and think there's numerous factors at play but think it's ultimately that she's basically a vocal jazz artist (which isn't the most popular type of music in general) who has a very unconventional voice that a lot of people really get into. Have talked to people who say they appreciate her talent but that her voice is oddly masculine and even in the realm of vocal jazz, she's far less hooky and/or accessible than earlier artists from the swing era like Billie, Ella etc.