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It seems like there's a three-way connection that forms in a musician's head between the note on the page, the sound the note makes, and the muscle memory for playing the note. Each connection is strengthened by different types of practice, and supported by each other, but often with the way we teach music the kinetic is a proxy between the aural and the visual; this is especially true of people who learn mechanical instruments.

One way to boost the aural/visual connection (when you already have strong aural/kinetic and visual/kinetic connections) is to pick up instruments that are very different from the ones you already know; I would think this is the goal of music education programs requiring basic proficiency with piano and singing, regardless of the student's main instrument. Once you have to learn a new set of muscle memory associations to go from the same note on the page to the same note in your ear, it starts to break down the strength of the muscle memory associations.