Writing is one of the two most important skills a student can learn. The other one is reading.
This in no way implies that everyone who teaches a student should be teaching those things.
ETclarify:
At university level (and at least in my country: yours is, as I understand it, a little more prescriptive, but not much) students, not professors, are responsible for the overall balance of what they learn. Universities, and professors in universities, are best regarded as resources that students can use to help them learn the things they've decided to learn. (Eventually, a student who has learned a given set of things to a reasonable standard will be awarded a degree certificate that summarises this and a transcript that gives more detail.) During their studies, students choose courses based partly on the published learning objectives of each course. The job of the person teaching a given course is to help students to achieve the learning objectives of that course - not to prioritise something else, however important, over those objectives that the student has chosen.
As far as writing is concerned, students at my university are required to come in with writing skills good enough to make themselves understood. Some students may wish to improve their writing skills; they can choose courses that will help them do that. The majority of the students I meet already have, when they enter university, writing skills which are more than good enough to equip them for the careers that they wish to follow. For that reason, I would not myself be in favour of changing the regulations to force all our students to take writing courses, let alone changing the way we teach courses so that more effort is spent on writing at the expense of subject content. That's not to devalue the teaching of writing.
If someone has to write prose for your class, you have a duty to make meaningful corrections. Otherwise, you're just assigning busy work.
(a) That's simply not true: students can learn a huge amount - both about how to wrote prose, and, often, about the subject they're writing about - from writing prose that isn't corrected by someone else. (b) One can make meaningful corrections to a student's work without correcting their writing, per se. One can correct the content, even!
From what you've written here and what I've seen/read, no one wants to seem to teach anyone how to write because they're too busy teaching other "important" things. Seriously? Are the students just supposed to figure it out? And teachers wonder why they get criticized?
Do you criticise the English professor for not teaching arithmetic, too? Are that professor's students just supposed to figure it out?
Respectfully, your answer came across as a bit petulant and as excusing all teachers and professors who don't want to teach students how to write.
Respectfully, your answer suggests a lack of understanding of the range of learning objectives of university courses.
. There are remedial classes you have to take before taking English composition (or the ESL equivalent) and up front testing, but while most writing heavy classes (say, history vs. color theory) recommend waiting until you have passed English composition a lot of students ignore the warnings.