I agree with Chet in many ways. I am someone who came from a classical training background. I learned to read music, I learned music history and theory. When I first started to play by ear, I was terrified - frozen. It took some time to learn to depend on my own skills as opposed to depending on the piece of paper. That was, as Chet was saying a lot of repetition in hearing the music.
I have also learned to incorporate knowing theory and reading music to be an asset when I play music by ear. I can hear intervals, relative pitch. I can use that to my advantage when listening to what I want to learn.
To me, when I meet someone who has become adept at learning by ear I am envious. I think they are somehow "closer" to music than I am. I also think someone who can learn by ear has more freedom and leeway with the music.
This conversation reminds me of the lyrics to a Louis Prima and Keely Smith song 'The Lip'...
And when they ask me can I read I say
I read a little bit, but not enough to hurt me none.