I live in Ireland, in the EU, and I'm fairly sure all the eggs in supermarkets here are washed. There's never a spot of dirt on them. And we always refrigerate, as does everyone I know
My understanding from such conversations is that eggs in the EU are definitely not washed.
Supermarket caged-hen eggs are generally clean in appearance due to the lack of items that might otherwise stick to the them.
I have found free range supermarket eggs, on the other hand, to sometimes have small features stuck to them.
I'm not sure what accounts for the generally clean appearance of supermarket eggs. Maybe eggs are brushed in some manner to remove obvious dirt. But the washing of eggs is certainly not a legal practice in the EU.
It's uncommon but it happens - they aren't throwing out the dirty ones.
In the other hand, you can have perfectly clean eggs if 1) you use a modern nesting box designed to hide the eggs and 2) provide independent sleeping areas higher to discourage the hens to sleep in the nesting boxes.
You could also scratch the surface with an old credit card or a knife but is better not to use water. Storing eggs in the fridge is also convenient, eggs shells shouldn't be in contact with other eggs.
I have no idea what the most common approach is. Eggs are not in the fridge at the supermarket, so why they would suddenly need to go in there once you get them home, I'm not sure.
Edit: The egg boxes are stacked outside of refrigerators at room temperature.
No, they're not washed. Lack of gunk is due to technique (or just cleaning mechanically) https://www.fsai.ie/faq/egg_washing.html
http://hoaxes.org/weblog/comments/artificial_dirty_eggs
"Artificially Dirty Eggs, 1973, the Dutch egg industry"