If I Ain't Got You is barely a decade old and No One isn't even that. Songs have to be judged over a long period of time to be deemed classics and, quite frankly, I don't see it for either one of them (though I do greatly prefer No One over Fallin'). Empire State of Mind isn't really Alicia's song, though I guess I can see why one would consider it such.
Also, and I don't know where this myth got started, but having had your song get covered on a reality singing competition does not mean your song is a classic. It means one person liked it enough to choose it for a performance.
It means one person liked it enough to choose it for a performance.