I've worked in a cold store way back. Like, a big warehouse filled with frozen items.
Say products needs to be maintained between -20 and -28C. That 8C is a massive amount of thermal energy. If you'd just cut power, say temperature in the cold store goes from -26 to -21C in a day (for a large cold store, probably less. Volume vs. surface area!). That means as long as you observe the outer ranges, and know how fast the store warms up (when not cooled) you can pick any time of the day to run the cooling systems. The mass of frozen product inside is your battery.
Connect to a bunch of solar panels on roof or nearby solar/wind farm, and you simply run cooling systems when that power comes up.
Versus: add battery storage & run cooling 24/7 to remain as-close-as-possible to optimal temp.
Similar things can be done with many factories, logistics, storage of thermal energy, charging EV batteries & more. Battery storage just gives more flexibility.
It's just using power in a smarter way. Not ditching modern comforts.
In the case of your freezer example, the freezer is a form of energy storage. Similarly a battery, or a phase change heat battery, are other forms of energy storage. Energy storage is important for the obvious reasons of being able to decouple time of production from time of consumption.
Modern humans built all of civilization on their ability to decouple time of production from consumption.