Okay, no one mentioned Aaron Neville!! Very distinctive voice, no singer who made it in the industry sounds like him. There may be some undiscovered soul out there, but as it stands no one.
Some of the voices mentioned have soundalikes. Maybe not dead ringers, but still enough to nullify their distinctiveness.
Examples include:
Frank Sinatra-Tony Bennett kind of sounds like him.
Sting-Tony Lewis of the Outfield could sometimes remind one of Sting.
Tom Petty and BOB Dylan, whom I think sometimes sounded similar.
As I read this question, I was literally listening to “God Shuffled His Feet” and thought, he would be a perfect candidate for this question, but you beat me to it…