This’ll blow your mind, but I actually put the box on top of the fridge. It makes sense in my kitchen layout, but I understand how much of fridge-tease it is for them.

Eggs survive in the wild at ambient temp because when they are laid, a coating basically seals off the egg. Unfortunately, chickens have one hole, and they are messy animals, so there's often some poop, too. In many countries, this coating is left intact, and technically, you should wash eggs before using them so nothing from the shell ends up inside when you crack it. As Americans, we have bigger houses and bigger fridges, and we love convenience, so we wash our eggs prior to packaging. This means they have to be refrigerated.

Either approach works, but the important thing is not to leave washed eggs unrefrigerated.

This is actually a very big difference with the USA and the UK (and possibly most of Europe, not sure though). We generally store eggs outside of the fridge. On a shelf or in a pantry/cupboard for example.