Unwashed eggs have a thin waxy coating ("bloom") that seals and protects them. They can actually store in a container on your counter for weeks that way. My understanding is that this is the retail standard in Europe.
In the US, the retail standard is to wash eggs which removes the bloom and allows air to get into the egg and spoil more quickly. Therefore, US retail eggs need to be refrigerated to last longer.
Messy eggs should be washed and refrigerated.
Either way works and neither has a real advantage. Do whichever you want.
PS- I also do longer-term storage of eggs ("water glassing") to store eggs for the winter, but I don't think that was what you are asking about.
