Of course, there is no grand plan, and yes, a lot of notation is historical accidents. But my point is that attempting to "fix" it will probably yield a better notation, but not the "perfect" notation.

As an aside, df/dx treated a fraction is used as soon as second or third semester of uni when they learn how to solve differential equations using separation of variables, and physicists/chemists start using total derivatives for thermodynamics. I am not aware of notation different from df/dx where these subjects would be just as clear.