Ideally. But when I took my cross-discipline gen-ed requirements, I was pretty amazed how little & how low-quality writing was expected of at least some of the humanities first & second years. Not much chance for growth when assigning a two-page paper is enough to provoke upset.
I also noticed this in my undergrad. In my second semester gen English, a 5 page minimally researched paper was enough to get people pretty upset, while in my hard science courses, it wasn't uncommon to turn in 20-30 pages every couple weeks.
Just as a clarification: Why do they ask for a minimum word count (or space count for that matter) and not for a minimum quality of the content. If students can accomplish the same with less words, then so be it.
I once had a professor who assigned regular essays with a maximum length of one properly formatted page. He was quite demanding, and I think I probably learned more about writing from those than most other multi-page assignments. He was also probably the most brilliant professor I'd had.
