Many recipes I've seen call for beating a tablespoon or so of water in with the egg for an egg wash.
What is the effect of adding the water to the egg wash when baking?
The proteins in a fresh egg are too viscous, even when thoroughly beaten, to wash a baked good.
The water thins the proteins so you get a nice glaze instead of a layer of scrambled egg.
Older eggs have sometimes degraded enough that they don't need the water but it is easier to always add water than to make a subjective judgement on the state of your egg proteins.