> Nope, they exactly allow the notes to show scale degree relationships. Without key signatures, music in any major scale other than C would be very confusing as the regular scale notes would be marked with accidentals.
Presumably, they have in mind to straightforwardly eliminate BOTH key signatures and accidental markers; e.g., a staff in which adjacent positions are always one semitone apart, and all pitches and intervals between them are thus always directly indicated without need for reference to a key signature for decoding.
There are pros and cons to this scheme (as it privileges indicating pitch relationships over, as you put it, "scale degree" relationships), but at any rate, it would not involve confusing accidentals, nor any significant difference between working in C major scale vs. any other (even less bias in favor of C major than the current system!).
A staff with a separate line or space for every semitone would probably be pretty unreadable, and the places corresponding to non-scale tones would go mostly unused in most music. Besides, the key signature at the start is very useful to any experienced musician as it immediately tells them how the piece is supposed to be played. You can think of it as a header that tells you how the rest of the notation should be interpreted.
I don't think it's a coincidence at all that the common Western staff has five lines and four spaces - it's a small enough number that subitizing [0] is possible. After all, the notation has evolved to be convenient to those who need to read or write sheet music, even though it might look weird to a layman.
Presumably, they have in mind to straightforwardly eliminate BOTH key signatures and accidental markers; e.g., a staff in which adjacent positions are always one semitone apart, and all pitches and intervals between them are thus always directly indicated without need for reference to a key signature for decoding.
There are pros and cons to this scheme (as it privileges indicating pitch relationships over, as you put it, "scale degree" relationships), but at any rate, it would not involve confusing accidentals, nor any significant difference between working in C major scale vs. any other (even less bias in favor of C major than the current system!).