People in my program take Spanish. I knew one person who did creative writing. We actually have a class on consulting in a closely related department that you could manage to sell as an elective. I took some only faintly related classes in another department.
It's not easy, and it will add time (that's the true problem with a PhD, balancing 'Things I want To Do' and 'I want to finish') but it's doable. PhDs are also often much less "locked in" to coursework than undergraduates, especially after their first few years.
"The problem here is that the definition of a Ph.D. for you is extremely different from the definition of Ph.D. for most of your students. I think there's next to no one whose primary objective with a Ph.D. is to produce a piece of original research - it is always a means to another end: usually career-oriented."
I can't think of a single person in my program who wasn't fully aware that a PhD is about producing original research. They might struggle with doing that, but it's a known and understood requirement.
There's a career-oriented degree. It's a Masters.