Hmmm, good question. I just did a quick Google search, most of what I found had to do with store-bought eggs already in cold storage.
We're in hot, humid So Fla and even in the summer I don't always get to collect the eggs until nightfall. Though the warmer the weather the earlier & more frequently I *try* to collect.
Often I'll leave the egg basket on the counter for a day or two, esp if I'm busy or the refrigerator is already stuffed with eggs.
I don't wash the eggs unless they're soiled, and then do it before refrigerating, with hot water & a paper towel, and then make sure to dry them & refrigerate immediately.
I think that unsoiled & uncracked fresh eggs will stay safe to eat at room temps for several days or more, the bloom is supposed to protect against bacteria. Many recipies call for room temp eggs, so these would work best for those purposes, since they've never been chilled. But chilling makes eggs age at a slower rate, so unless you plan to eat them soon, I think it's best to store them in the fridge. Either immediately or within a few days.
I wonder if fresh eggs stored at room temp for only a few days would make as easy-to-peel hard-boiled eggs as older eggs kept in the fridge? This will have to be my next experiment.
Also, is it a bad practice to take fresh eggs from the fridge, let them warm to room temp, and then re-refrigerate? Sometimes I'll bring chilled eggs to friends or customers away from their homes & they aren't going back home right away. Is it all right for them to leave those eggs out for a few hours, then put back in their fridges?
BTW, I write the date of lay in pencil on the end of each egg so I'll know their age & can use the older ones first. Other folks who receive or buy our eggs will ask "is this a code for which hen laid which egg?" Not knowing or noticing that the carton is filled with eggs of various sizes & colors, all with the SAME number on them. I tell them, with a sigh, that this is the most difficult part of keeping laying hens, teaching them to write those numbers on their eggs. Besides getting them to lay them in those cartons, of course...