I listened to some of Sia's songs, most of them are really depressive and I felt that there is something wrong with her. Then I googled a bit and saw that she tries to hide her face. Now I see where it all comes from.
she hides her face because she wanted to add mystery to her character because she thinks that modern pop lacks that. She once said on Ellen's show "there's pictures of every celeb even at the dentist".
Though, her voice is truly amazing