It's actually pretty common notation in a lot of fields, and mathematicians frequently switch between whichever of these notations is most convenient for a particular problem. Your point of course still stands for why isn't it the main one used in Calculus 1 courses, but it's common in differential equations courses in my experience (and PDE's often simplifies it further to just have D_x f as f_x). And many times where the "derivative" is not necessarily the "calc 1" derivative, you use notation similar to that, for example the covariant derivative [1] is sometimes written like that but with a 'nabla' instead of a 'D'. Some authors even use 'D' for covariant derivative along a path.

[1] https://en.wikipedia.org/wiki/Covariant_derivative