Since I changed my assignment to reflect that the students get to choose what they are drawing/painting/etc. I have far less work thrown away. I set the criteria for the assignment and they find a picture that meets that criteria.
Any work not picked up at the end of the semester get put into a pile in the staffroom and the teachers get to take stuff to decorate their classroom. I have to stress that it is for school decoration not home decoration (only had one woman argue with me) but at least the school gets more student artwork displayed. The kids are shocked walking in and seeing their work on the wall but it is a way of decorating my somewhat stark school.