The required improvement would achieve:
When a student submits an assignment, Moodle can automatically return one (or more) files to the student. The file(s) returned are specific and linked to the assignment. The files are prepared and uploaded to Moodle by the teacher.
The assignment may remain available for marking, grading and further feedback by the teacher.
At the moment, when a student submits a Quiz he immediately receives automatic feedback previously prepared by the teacher. The teacher then marks the quiz and can send further feedback. A similar system is needed for Assignments.