> (And for that matter, if students in my Ph.D. program want to enroll in courses in business, writing, or anything else, they can.)

True this. Almost every university I've dealt with loves for their math and science Ph.D. students to take a business class or two. But requiring it would be outside the point of a Ph.D. Honestly, most Ph.D. programs have a couple core classes, then they are pretty flexible about what classes you take as long as you can make up an excuse.

Additionally, one friend getting a Ph.D. really wanted a job in science journalism. He found time to intern for a newspaper doing the journalism while still a candidate. Plenty of others build up a portfolio just blogging on the side. If you come out of a Ph.D. wanting to be a writer, it's your fault if you don't have a well put-together portfolio.