I suppose some people buy the mugs mostly for the ICEES. It would be like buying the mugs to fill with coffee in the morning or soda in the afternoon and being told all that is available is hot or iced tea to fill your mug with. I think the only way around it is to not allow free refills of ICEE.Of course then people would fill them anyway and get by with it.
My sister used to work these machines for her job during her High School years. On any given hot day, she would come home with stories about how the machine "broke down" again from over use. These machines aren't made for continuous use. If you plan on buying the mug solely for ICEEs you will most likely be disappointed. Purchase for the beverages and consider the ICEEs a bonus.