I was taught that fresh eggs do not need refrigerated for several days if the storage temperature is not warm. We kept eggs on the screen porch, not in the kitchen. We just wiped off the fresh eggs when we gathered them and my mother washed them right before use.
Modern store eggs are washed before they leave the farm which washes off the protective coating the shells have so they do need to be refrigerated.
Actually a fertile egg that is not washed keeps for a couple weeks in cool weather. Washing it drowns it, and it will rot quickly. It is how a chicken who only lays a single egg a day can raise a whole clutch of baby chicks.