Graded assignments are one of the many ways to teach responsibility and quality. Graded assignments are necessary because if assignments were not graded the quality of work would dramatically decrease. Each grade level teacher would have a harder time than the last as certain students would not learn the material necessary for advancement.
Students and teachers need a system through which they can assess students progress. This doesn't necessarily require a grade system, but that seems to work pretty well. A numerical grade can show a student exactly how much of the material they understand and show them what they need to work on, thus potentially leading to improvement.