That's because music doesn't usually use a 12 tone scale, it uses a heptatonic or pentatonic scale, and Western musical notation is pretty good at representing that.
A single piece may not, but taken as a whole body of work, dodecatonic scales are the norm in most music today. So rather than have to say "this 5-stave notation represents the key of E-flat in this particular case", a 6-stave representation would be key-agnostic. Not all note positions would be needed in a given piece, but all instruments could play the same piece in the same key from the same notation. The notation would be clearer due to the lower degree of visual "compression" and the lack of need to notate exceptions to sharps, flats and naturals indicated by the key. Makes total sense. But it will never happen, because reactionaries would object, as you did.