https://www.youtube.com/watch?v=avUXnAMpFoo
True, her voice seems like is close to cracking but that doesn't bother me a bit and from my point of view, what counts is her power to deliver. You may not like her but surely cannot stay indifferent, 'cause this lady delivers strongly.
As for her personal life that was tightly wrapped up around her singing career, I can understand that this can bother people and can affect on the way people see her but could Billie perform the same if she hadn't had the life she had? It seems that her singing is nondetachable from her personal life. Maybe people like her precisely because of her 'crack in the voice'. The perfect imperfection.
Orpheus, thank you for the explanation of being 'jazzy'...I can imagine your jazzy friend. In Croatian language, the word 'jaz' (with one 'z') signify the amount of distance between the people or it can literary signify the great hole. For example we say...there is a big 'jaz' (distance, hole) between us.
So maybe your friend is slightly distanced towards everybody else and has the mind of his own, his own and original look or behavior. And that makes him jazzy... :)