> For example...in the key of aminor when you make the five chord major to create a resolution back to i (aminor) you raise the 7th scale degree. That means the G becomes G#...Ab is the same pitch but writing it that way is wrong. An EMajor chord is spelled E G# B, not E Ab B. Now if you spell that as 9 0 4 you have stripped all context out of the music. Musicians aren't just player pianos, they analyze the harmonic structure of the music the inform phrasing, shape, tone, volume, and pacing (acelarando, decelerando, ritardando, etc).

I feel like those are idiosyncrasies that feed into eachother i.e. you need to have 2 notations for same sound just because other decisions made it so there is no extra info passed other than in b vs #

So alternative notation could still make it clearer/"mathematic" but would essentialy need to include all of that, and for that as you said, you need people with wide experience about music and for them, they already are fine with standard notation so for them it wouldn't be an improvement because nicer learning curve doesn't matter once you learned it.

Classical keyboard layout is kinda similiar in opposite way here; beginner can just slap some white keys and get something musical and they can learn from there, while various chromatic keyboard layouts might have some nice benefits (chords being "same shape" regardless of where you play them), it is harder to start on it.