> They are only "proficient" in a very limited sense, then. I'm sure we can argue semantics here, but a musician needs to understand the concepts that govern music. And these concepts can only be understood and visualised by using notation.
That's pretty narrow. Some people aren't visual thinkers and don't need to see something on the written page to understand it. I personally know several musicians who have a deep understanding of music theory, but don't read music. You can explain and understand modes, transposition, chords, etc without having to write it down.
> I personally know several musicians who have a deep understanding of music theory, but don't read music
"don't" or "can't" read music? I think this is a critical distinction. If the answer is the latter I would still argue that they cannot have a deep understanding of music theory, since a major component of music theory is generally accepted to involve understanding notation.
Edit: I can accept that there are many aspects to music theory that go beyond just notation, but I am skeptical of 'deep understanding'.
That's pretty narrow. Some people aren't visual thinkers and don't need to see something on the written page to understand it. I personally know several musicians who have a deep understanding of music theory, but don't read music. You can explain and understand modes, transposition, chords, etc without having to write it down.