I would happily have banned pencil cases, not for the reasons that the school quoted above has given, but because they took up so much space on the tables/desks where the children worked, not leaving room for exercise and text books, apparatus et al, and were the cause of endless fiddling and playing about, swapping, 'borrowing' and losing, (not to mention one notorious case of assault with a metal tin pencil case, fortunately by a child no longer in my class, or school).
All a child needs to work is a pencil, pen, ruler, rubber, and pencil sharpener, all of which are provided by the school, and kept in pencil pots, baskets on the tables. Rows of felt pens, crayons, smell pens, luminous glow in the dark pens, magic markers ,magic erasers etc, etc, etc are fine for art work and can be kept in the cloakroom, tray etc; but they are not needed for everyday work.