The most important thing, in my view, is for professors to carefully line-edit each draft, then require the student to revise. That takes a lot of time, but there is no shortcut.
The solution that cuts the Gordian Knot would be to restore English throughout K–12 so that students don’t get through high school without reasonably good language skills. That won’t happen, because of the animosity in education schools toward all those fussy old rules.
The only way to address writing is to give line-by-line feedback. We cannot assume that students know what good writing looks like. Every time students pass a written assignment at any level with subpar writing, such poor performance is reinforced as acceptable and the poor writing ability become the next professor’s problem.
To the extent I learned to be a better writer, it was because much of my writing as a lawyer was prose-like – Annual Reports, Prospectuses, etc. – and every line was read and reread, reviewed and edited. You quickly got past pride of authorship, but if you didn’t become a good writer, you started losing the good projects and better clients. I know in my class and in the IB world, grammar and style are not important, and when I grade economics papers, I focus almost exclusively on content and not writing quality. I wish it could be otherwise.