Interesting how a cover can bring new life to a song or act as a lens through which previously unnoticed or under-appreciated aspects/qualities can be perceived/appreciated.
Having said that, for me it’s a fairly rare occurrence in popular genres There are plenty of (technically) competently-sung covers that sound generic because the artist simply lacks the creativity or vision to make it their own. And vocal technique can be a liability if that's all an artist brings to a cover.
Of course, it’s not just about the artist. If the listener has heard the song in its original version so often that they’re sick of it (thanks to "classic rock" radio formats, for example), then the ear may embrace a cover out of sheer relief.
There are some artists who, by virtue of a particularly idiosyncratic vocal approach manage to make any cover sound new. Richie Havens, Joe Cocker, Taj Mahal, Willie Nelson, Janis, Leon Russell, Lucinda Williams and Nina Simone immediately spring to mind.
I’d argue that Jazz, as a genre based in improvisation/reinvention is a treasure trove in this regard.
I’ve never cared for the Classical vocal esthetic but perhaps someone who is a fan can share their perspective