Ask yourself a simple question. Suppose an instructor desperately wants to communicate with her students that she cares more about the quality of their writing than about the volume they produce. How does she communicate that preference to the students in a meaningful way?
Let's add a complicating but pretty obvious factor. If an instructor gives a deadline for the project that is say a month away, human nature suggests that most students will do little to nothing on the assignment till the deadline appears in the offing. This is human nature. Students also may not realize that to get a good quality product, they have to go through multiple drafts. One and done often doesn't cut it.
Once students do kick into high gear and get cranking writing their piece they can then form a sense of their own about how high quality a product they are producing. Students (at least the ones I know) don't maintain that intensity for the entire semester, and when they are in less intense mode, they are much less sensitive to suggestions about how to improve their work. So most efficient for their own learning is some rapid iteration between student and instructor during the interval of intensity. This is why I don't believe having deadlines for drafts that precede the ultimate delivery is the right way to go.
I think it is actually better for learning to set up faux deadlines that are communicated to the student as hard limits. They are still intense at or soon after that deadline. As instructor, you now have their complete attention, so you can push for making their work better with suggestions and further iterations past the deadline.
Then there is something else as instructor you can do to enhance quality of the final product - give the ultimate decision power to the student regarding any recommendations you make as editor, author's prerogative if you will. If you have a little email thread with the student about the suggested changes and explain the why behind making them, then the student is in a position to think through the suggestions and give a why back on not accepting them or make the changes accordingly. The students will then have some ownership of the work and if capable should produce good stuff in this setting.
It is time intensive for the instructor to be reading and commenting this way, but it certainly is a good way to have dialog with students on a one-on-one basis, conversations that the students probably wouldn't initiate otherwise. And the deliverable can then be something all are proud of.