Problem with not refrigerating eggs is that they start change after a few weeks, going bad is not the proper term, less fresh would be more apt, another few weeks and things start turning green (Dr Seuss did not invent those green eggs) and are still not bad in the sense of not being able to eat them but they are far from appetizing in anyway. Modern world requires eggs to last longer, could be 3 months before an egg hits the shelf at the grocery store, so we wash them and keep them refrigerated.
Salmonella is still on the shell of washed eggs, most comes off with the bloom (the coating on a fresh egg) but the bloom is not perfect. So we keep our washed eggs in the fridge to slow growth and store the eggs in a carton which can absorb anything which condenses on them when you take them out of the fridge.
The best by date on an egg carton mostly refers to raw consumption, moisture in the fridge and moisture that condenses on the shell when you take them out will slowly seep into the egg and carry the salmonella into the part we eat and where the salmonella can grow and multiply to dangerous levels for raw. If you have gone past the use by date you may want to skip those soft boiled or sunny side up eggs but they are fine for more firmly cooked eggs and probably fine for soft boiled and sunny side up unless you are well past the use by date.