I am an almost entirely self-taught jazz musician. I learned to read notation begrudgingly, assuming it to be an archaic hurdle put in place by snobbish classical musicians. My view of classical musicians has not changed, but my view of notation has.
A lot of people think that programming languages are a similar archaic hurdle and set out to build a visual programming environment that will be easy for beginners to use. Somewhere along that journey, they invariably realise that a) syntax is one of the easiest parts of programming, b) there is no good visual metaphor for recursion and c) the Deutsch limit is a cruel master. You can do simple scripting with a box and arrow diagram, you can teach kids to blink an LED, but you can't write a compiler.
The advantages of stave notation (and the disadvantages of alternative systems) are non-obvious, but they are very real. Critiques of notation usually sound like "command lines are stupid, everything should be a GUI" - they're not wrong per se, they just miss the point.