I think there has not been sufficient attention given to two important facts.

First, that sheet music is for the purpose of communication between musicians, who may be separated in space or time. (As pointed out above, you don't have to read to be able to play). So the rules for a notation must be fixed.

Secondly, and mainly important for chordal instruments, the type of chord can easily be seen by the SHAPE it makes on the staff. Check, for example, a dominant 7th - it will ALWAYS look the same, however much you transpose keys - it just moves up or down on the staff. This is one of the lesser-known beauties of the notation, and makes sight-reading easier than it would otherwise be.

If you now decide to write a B# on the staff as C, then in the chord of G# as mentioned above, ITS SHAPE WILL BE CHANGED, and the chord will no longer look as it should.