There are a great many annotations to individual notes: lines, accents, staccato dots, slurs and brackets, dynamic markings etc. etc. that indicate timbre, and you've always got the fallback of just writing out what you want, and it's even acceptable to not even use Italian these days!
Imagine it as a piano with all alternating black and white notes, no gaps.
Now there are 6 white and 6 black notes per octave.
You would only have to learn two positions to have learned all scales and all chords (like sliding moving a bar chord on a guitar).
I don't know that it would be better. It might be soulless but it also reduces the redundancy of learning harmony and theory and suddenly jumping up a key is as simple as physically moving up a key.
You'd also need different keyboards and notation if you start considering music not built around the octave.
Really interesting reference. Will definitely read more into Jankó.
Interesting almost every pro musician I know uses the chord numbers to convey this information orally more than they use the note names. And when I did degree in jazz it was always focused on the numbers.
Musicians clearly understand the patterns, but it's beginners that I'm concerned with. After decades of study / practice most systems are workable.
I can see why it's not easy to give up.
Where it suffers is in notating timbre, so you get things like the orchestral score which isn't really all musical information but also leaks implementation details.