There are singers who are, for many of us, an acquired taste. The tone and timbre of their voices are things for which one is challenged to endure as they squirm and writhe through the first few, nascent listenings. Willie Nelson, Tom Waits, Billie Holiday, Bob Dylan, Louis Armstrong, Johnny Cash - these are/were singers who would probably not even get past the local audition stage of American Idol (and that can't be a good sign!). But if one is patient, and survives early exposure, the overall, musical quality of their voices (no doubt profoundly helped by the quality of the strong material they recorded/record) eventually come through, and there can be great payoff and rewards for the listener.
Astrud Gilberto comes to mind as a singer who would fit into this category - one who does not have a particularly strong voice, and there is occasionally the feeling that things are about to come off the rail, vocally, so to speak. But I bet she wouldn't forget the words to America's national anthem, no matter how nervous she was (and despite not speaking English as her native tongue!).