I have one pair of birds that get an egg a day (usually a banties egg, but now it's a standard since it's cold here and they can use the energy). They're a calico princess pullet and a naked neck cockerel that just seem to need that extra protein from eggs. Otherwise I normally don't make a habit out of it unless there are weak chicks with a broody that might need assistance
When I'm raising chicks, I feed them one scrambled egg per day. It helps them learn to not be afraid of my hands and it's also good for them. When they are small it can take them 3 days to eat that one egg! (I hold a small container with the eggs inside and when they stop feeding I remove and refrigerate what's left). When they get to be about a month old, they don't get their egg anymore unless I have too many.
Yesterday I had a ton of pullet eggs and needed to use them up so I scrambled them up with the eggs shells and fed them to my adult flock. They were so happy!
I feed mine scrambled and any that get cracked in the nest - I have done this for years with many different chickens and none have ever offered to eat their own until I break it open for them.
Others have given great advice - egg is good, but moderation is always key