Of course it is not possible to study effectively at university without being able to listen to lectures and take notes, read books and journal articles or take part in seminar discussions but almost all assessment involves some kind of writing, often under time pressure in exams. It is also the hardest skill to learn to do fluently, for anyone not just second language learners.
Writing is not much valued in other types of English courses, where language learning is more often conducted through reading, listening and speaking. If writing occurs at all, it is used to reinforce grammar points or to express personal preferences and opinions. Students may be asked to write genres that they might never need to write in their own languages, e.g. newspaper articles, poems, personal diaries or opinion essays.
Writing at university is also very different from these personal or creative types of writing. It is almost always based on material from sources, such as books or journal articles, or data collected from surveys, observations or experiments. It has a specified purpose, e.g. a question to asnwer, and a particular audience which has expectations about the structure of texts and the style of writing. It requires students to be able to manipulate complex noun phrases in simple sentences rather than complex verb phrases in compound sentences.
Both students and teachers new to academic writing often complain that it is not creative. However, the creativity lies not in the unusual choice of vocabulary or sentence structure but in the ability to make writing transparent, like a pane of glass to allow new ideas to shine through.
In another post Irina argued that any teacher who wanted to develop professionally needed to understand EAP approaches. I would take this further and suggest that any teacher who wishes to teach EAP needs to have experience of writing academic genres.