I streamed Mary Coughlan singing Billie Holiday songs and I had to turn it off. I don't know what her problem was. I read that she drank a lot and has had a rough life.
But when I play other songs by her, she's got the feeling that jazz singers need. Her voice sounds like a jazz voice to me because she sounds like she sitting next to me and I can feel her heartbeat.
So, try one more and see if you don't think she has a jazz singer's voice.
https://www.youtube.com/watch?v=8LEkUeIoWr0
BTW, still watching Ken Burns' Jazz series, I got to the part where the better musicians like Parker and Gillespie lose most of their audience playing be-bop. There is a real rift in which the be-bop musicians look down upon the old swing musicians who still draw crowds. The narrator said that the be-bop musicians (almost all black) thought of someone like Louis Armstrong as an Uncle Tom.
So, even among "jazz" musicians, some didn't think others were. Louis Armstrong is shown in the Hollywood Bowl singing a song that makes fun of Parker et al, saying be-bop closes clubs. I think that rift still exists, where some people think that successful jazz players like Diana Krall are not real jazz. I've seen Diana Krall live several times and watched the older jazz musicians backing her marvel at her piano playing. She can do some mean riffs. So can Patricia Barber. If you listen to her piano playing she's as interesting as any jazz pianist I've heard playing today.

