Oh good god :) Picking up writing from reading the average paper is likely injurious to the health of your future readers. Few papers are well-written and you're likely to unknowingly pick up bad habits from reading the average paper. If your advisor was actively training you in good writing and providing you critical feedback on sentence construction, paragraph organization, the flow of ideas from one section to the next, then sure, you wouldn't really require a class. But I doubt the average advisor has the bandwidth for such feedback, esp. in my field of biology.

In the context where I taught, most students coming into the PhD program had no training in writing whatsoever. The first round of essays that people turned in were typically very poorly written. Most folks really needed the training in my view.