IMO Taylor doesn't have a "Billie Jean", but few do. But that's beside the point. She might not even have a "Hit Me Baby One More Time" or "Real Slim Shady" or "10,000 Miles". That's not necessarily due to the quality of her songs, but moreso due to how insular and atomized cultural experience are these days - you can fill stadiums, and be the biggest artist in your field, and yet there the majority of people would not recognize your song, because in this moment everyone lives in their own technologically carved out algorithm. I'd bet many Swifties in this thread would feel similarly about Beyonce. How many people here could recall a single tune, or hum more than a chorus or two?
Though, I've had a feeling, even though I don't think Taylor Swift has anything close to, say, "Falling in Love With You", "Ring of Fire", "Born in the USA", "Piano Man", "Sympathy for the Devil", "Bohemian Rhapsody" - the list goes on and on - she might very well be the last celebrity that we all at least recognize. Being that person, moving forward, will only get harder and harder as the culture continues to fracture.