How can we promote better writing skills in academic education?
In my lab, we were required to produce three-to-four page white papers, including figures, every time we presented at a lab meeting (approx. every 6 weeks).

This had two significant effects. Firstly, it forced the student to write down their progress, which was invariably ridiculously useful when the student actually started writing their thesis. Staple together a few of these sections and the methods, and often a good part of the background, was written for you.

Secondly, it gave everyone a chance to practice their professional writing in a casual lab setting. No one felt threatened and everyone improved. We would even review the articles being written by the lab professor, as there were always improvements we could suggest to him as well.

I strongly recommend this practice.