This question asks if the accidentals are not "additive" (i.e. placing a sharp on F where the key signature already contains an F sharp would result in an F double sharp, and placing a flat on F in the same key would mean F natural), but it does not explains why they are not.
At least in my opinion, additive accidentals would have the following advantages:
- there would be no need in a separate natural sign, since cancellation could be expressed with the opposite accidental.
- double alterations would be used much less often (in the most cases, double sharps and flats are used to raise/lower a note which has been already sharpened/flattened, not to raise/lower a natural note by 2 semitones).
- accidentals would stay the same upon transposing. In particular case, all scales would be written in the same manner (e.g. a harmonic minor scale would always have a sharp on its 7th degree, regardless of the key signature).
- the notation system would become more logically coherent (for example, a note with a sharp near it will always sound a semitone higher than the same note without this sharp - i.e. if we erase this sharp, the sound will be always a semitone lower)
So, why it was "decided" to stick to the current system?
P.S. I know that "why" may not be (or at least sound as) a correct question for the StackExchange format (because it associates with primarily opinion-based questions; so I apologise in advance for the question being out of format), but I believe that the objective reasons for this particular topic should exist (because the notation system is (almost) worldwide-spread).