Being dirty doesn't magically make eggs last longer; these eggs don't need to be washed because they're not very dirty.

While I can't speak for all European eggs, you can store UK eggs for longer, outside the fridge, because they are likely to be significantly less dirty at the point of collection, the chickens they came from are less likely to be infected with salmonella, and because they are not subjected to a damaging process (washing) that aids the transfer of harmful substances from the outside of the egg to the inside.

Its a chemical layer that's removed by washing, that makes eggs need refrigeration. Until washed, they're an antiseptic capsule. After - bacteria can enter through exposed pores in the shell.

They can be sold dirtier because the chickens live in a cleaner environment. They have to be washed in the US because they're not sellable otherwise.

What do you mean be "store longer"? I've stored average American eggs in the refrigerator for multiple months without a problem (I only use them on the rare occasion that I bake something).

I am under the impression that European eggs are not refrigerated. My understanding is that once you refrigerate an egg, the membrane separates from the shell, requiring that you continue to refrigerate it, as the egg is no longer properly sealed. Since American eggs are refrigerated to begin with, you need to continue refrigeration.