Dear Rev M,
It's a standard behavior, Material Classification is mainly used to classify the material, to Use additional data that belongs to Material could be link to that materiel other than 40 characters, & moreover you will never ever get this additional on standard report but you can search additional data via classification search string to get the report.
You can only search material in Sale Order and Quotaiton and fetch that field only on Out put of Quotation and Sale order. Material can search by the mentioned below screen shot.
