The Amish don't put faces on their dolls either. This is in keeping with the Old Testament commandment against making graven images.
The reason Sunbonnet Sue doesn't have a face is because when she was originally created, her hat covered her face. When the SBS theme was carried over to things that were 3 dimensional, like door stops, no one could make a face because no one knows what her face looks like since it has always been hidden by her bonnet.