I dated a guy who was truly tonedeaf. His "singing" was monotone. As someone who has perfect pitch, it was torture for me to be around him when he was attempting to "sing".
Make a different argument. This one isn't working.
The argument may or may not be working, but the underlying assertion is true: Frank Sinatra couldn't carry a tune, and he couldn't sing in key.
Again, the source of his popularity is a complete mystery to me [which is why I posit some sort of weird ethnic boosterism] - he wasn't even particularly handsome [frankly, he was rather an ugly fellow].