The problem with learning things visually is that it gets you thinking with your eyes, and in music, your eyes are the biggest liars in multiple ways.I don't really know instruments or music, but people do learn in different ways. So saying that one way is the correct way to do it isn't always true. Like with your math example, I have anxiety when it comes to math (because I possibly have the number equivalent of dyslexia), and sometimes having the answer actually does help me learn easier. Because then I have less anxiety, and can work backwards to see the process more clearly. Just because stuff works one way for some people doesn't mean it works that way for everyone.
First, if the instrument is tuned differently than normal, like an open tuning, then shapes aren't going to work anymore, even if your fingers are in the "right spot" because now the instrument isn't tuned like normal, but to a chord, so if you learned a scale shape, and nothing else about it, it's not going to help in this situation.
Second, listening with your eyes ignores a key aspect all musicians rely on, ear training. By SOUND I should be able to identify what a minor scale sounds like, a dominant 7th chord, or what have you. Ear training is super important, especially when it's used to train what certain intervals, chords, and cadences sound like, so when you go to write music, you can recall that sound, regardless of key or tuning.
Third, when choosing what equipment sounds better when our eyes are running the game, people tend to choose famous brands, regardless of what their ears told them they preferred. The explanation is simple, they listened with their eyes, not their ears. So setting up a sound that's unique to you becomes problematic when you're not really listening to what you like about a particular piece of equipment.
This is why I don't like telling people where to put their fingers, because on a guitar, one note can be played in multiple places, notes can be arranged how you so choose, and, when the tuning changes, the shapes you learned are no longer useful.
For music, listening with your eyes is unhelpful, so I try to get people to think with their ears, not their eyes, because do you watch music with your eyes? No, you listen to it with your ears.
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