A funny thing about the dots Ivan, is that I have almost always needed them.
The only exception to this is when I have had to learn a song "by ear". I played with a Mexican dance band for about a year in the early 1980's. They had no written music. I learned the lead trumpet parts by recording the trombone player playing the parts during rehearsal and then sitting down for litterally hours repeatedly playing each part piece by piece until I had them down pat.
That being said, I played with a German polka band for over 10 years and still couldn't/can't play the Beer Barrell Polka through with out the music in front of me.
I feel there is just a difference in the way people remember things. The onus does not belong with the schools or instructors. I am not sure that you can even teach this in school. That is of course unless you are Professor Harold Hill and use the "Think System."