OK, fascinating thread. Firstly, I understand why you like your preferred selection. But from my take, what I hear is the difficulty with the meaning of the song. In every clip except Billie's, when it gets to the words, "That's got his own." there is a subtle yet distinctive avoidance. My view is that all the other words are understandable - the singer can get behind those - but at the precise moment of the critical words of the song, no one except Billie knows what it means, and thus they can't come in powerfully behind them.
The words speak of wealth - monetary wealth. But at the point of these critical words, the meaning of wealth changes dramatically - what is she talking about? Oh, I'm sure everyone has an idea about it, and yet having an idea is not the same as knowing intimately. Knowing from the bottom of your soul. Every singer has found their public voice through the good-auspices of a person in position of power, and they project that framework if you listen carefully. Billie is centred. Yes, so are some of the others, but no where near as much as Billie.
There is a tone in her voice which says, 'I sing because I sing'. All the others are singing for an audience.
To me, this song is Billie's song, even more than any other I have heard her sing. The others are singing a great song, as great singers or musicians, but only she is singing the song of her soul. She sings this song as if she is completely alone.