Raw egg is extremely nutritious, is a natural food for dogs, and does indeed help keep the coat in good condition.
Providing they are fed in moderation. An appropriate amount of raw egg to feed is one or two per
week. Feed a raw egg every single day and it will have the opposite effect - your dog's hair will fall out
That is due to the adavin in the egg white binding to biotin (a B vitamin) and preventing it being absorbed properly. Egg yolk contains biotin, of course, so it is balanced to a reasonable extent. Feed in excess though, and the excessive adavin will cause problems - like so many things in life, while a little is very beneficial, taken to excess it does more harm than good.