“Paying one’s dues” has a very different connotation to me than “Learning a skill.” The former suggests a tenure-based system of seniority and pay scales, rather than a meritocratic system based on skill level and actual output.
To me it just says you'll make less for a period while learning the ropes. I suppose there are situations where you need to be spending the time to empty the trashcans but I don't take it that way.