Refrigeration helps to slow any bacterial growth and reduce the chance the eggs turn bad. This is why commercial eggs are also refrigerated. Keep in mind, even if you leave the eggs unwashed, once you put eggs in the fridge, they cannot be stored back on the counter.
But how do you preserve eggs?!
That sort of depends where you source your eggs from.
Whether drying, freezing or canning, food preservation has been a massively important homestead tool. History tells us that food shortages happen and it's best to be prepared with an abundance of shelf stable items. The hydro can and will go out and whether you have a generator or not, it's possible it runs on gasoline and that too may be a challenge to access if times or weather are bad enough. How do we keep our families fed?
Growing up on the farm and having our food cared for out our own back door was a gift. Nourishing our livestock daily, watering and tending to a garden and then prepping and preserving foods for winter use.
Can you cook from scratch and grow your own food too? Absolutely yes!