No correlation at all.
Marianne Faithful was very good looking in her heyday and had a beautiful pure voice. And then there's Debbie Harry and Diana Ross. Whereas Janis Joplin had a great voice but..........
The Beatles main singers (John and Paul) were not that bad looking either.
Can't see any connection between good looks and vocal chords. Only thing I would say is that maybe those, who are particularly aesthetically challenged, might have experienced more pain and disappointment in their lives, which could give a greater depth to their performance.