Eggs do not really require refrigeration as long as you're gonna eat the eggs or use the eggs up within a week of purchasing them.
If you're not going to use the eggs or eat the eggs within a week of purchasing them then you should refrigerate them to keep them from going bad.
I have always kept eggs out on the counter and have eaten them before a week and they have always been okay and I've even had eggs left out at room temperature for 14 days and they have also been okay to eat.
Fresh eggs don't even need refrigeration as long as you're eating them soon but if you're not eating the eggs within a week then refrigerate them.
However if your house is hot and not cool in the summertime then you should always refrigerate the eggs to keep them cool.
Because the heat can spoil them.