A very interesting question and I'm sure the answer will vary greatly.

For me, a key factor is to get lost in the song. I recently listened to two tracks on the same CD by the same singer: the first didn't work for me but the second did. Part of the reason was that the first was played too perfectly: every bar was exactly the same length, for example, which meant some syllables of the song had to be stretched or compressed a little to fit the precision of the melody and the effect was, to me, somewhat mechanical. In the other track the words took precidence and the bars were slightly lengthened or shortened, driven by the words. I found the second much more absorbing.

SO there is a bit of contradiction here. When I hear a song without warning, I recognise the singer as Maddie, or June, or Norma, so clearly I don't abstract them away entirely. But when they sing, for me they do it in a way where they style does not distract from what the song is about.