how can thin walls be an advantage to the cells that store materials?

Answer 1

Materials can enter and leave the cell more easily and quickly, and the membrane can stretch and the cell expand to accomodate larger amounts of storage product. This is expecially seen in fat cells.

Answer 2

a thin wall mean a thin membrane in sense and so with a thin membrane the stored materials won't have to travel far to either enter the cell or leave the cell.