Using an appliance later is no more a form of energy storage than me "saving" air by holding my breath. Reduction in peak demand <> Storage.
On a hot summer day when I'm cooking in the house, running a load of dishes and trying to cool the house to a reasonable temperature - all before the guests arrive - Should the A/C wait for the dishwasher, which waits for refrigerator, which waits for the oven? Not in my house.
Storage - I'll gladly take some of that so my lighting and communication can be powered when the power is out. In that situation, the rest of those big loads can wait.