When laid they have an anti bacterial coating on the outside called the bloom.. that protects against bacteria entering the egg. "Washing" removes that coating and allows for more rapid evaporation of the contents inside.
The longer they stay at that high temperature (or even standard room temperature).. the lower quality the egg inside will be.. that is thinner white, shorter yolk, easier to break. Safety is not the issue when collecting CLEAN eggs daily and refrigerating afterwards.. practice first in first out method.
Egg float test may tell you how much air had been exchanged or how much evaporation has taken place.. helping discern the age of eggs. True very bad eggs may float.. but otherwise float test just subjects eggs to floating in water.. if washing.. use water hotter than the eggs as using colder water *may* suck bacteria inward.
If eggs are "dirty".. the should be washed and moved to the front of the line for use.. Also checked for cracks.. anything cracked and also dirty can be scrambled or fed back to the animals, chickens/dogs, etc. Clean slightly cracked eggs unwashed are just moved to the head of the line also.. in front of the whole washed ones.
Fertile eggs will not have development if collected daily.. most will start to show veins around 3 days above 98 degrees.
Hope this helps some!