Nothing really wrong with using an egg straight from the fridge, but the main reason to take them out of the fridge first is to improve the results as the enzymes and proteins in the egg are not meant to be chilled - think about where they come from and what they are meant to do . . . .
A hard boiled egg is less likely to crack if cooked from room temp. and one about a week old tends to give a better result than fresh. And don't add salt to the water in the pan as this draws out moisture from the egg while it is cooking.
Eggs, as the shell is porous, will also absorb odours from the fridge, so it is better to keep them in a cool, dark place - used to have larders one upon a time that were ideal . . .
Fresh eggs sink in a glass of water, older eggs float to the top - stale ones don't even begin to sink, so its an easy way to check the age of the egg.