I am sure eggs have contributed to Stanley's very soft shiny coat, .......... but I can't prove it.
I can. If I stop feeding eggs their coat-quality diminishes a bit. Less shiny, a bit harsher, more grease. Not by a huge amount but I definitely notice it.
Conker (25 pounds) gets at least one egg a day. (Yes,
at least one egg.) The Girls (50 pounds) usually get one each as well. Sometimes they get one every other day. Depends on how many eggs I've got and what the current price is. Right now they are on-sale for a killer deal so I've got a bunch. Conker and Juneau don't easily eat the shell so I either smash it up or don't bother with it. I do, however, take the time to peel the membrane out of it since I do whatever I can to keep Conker's joints healthy and that membrane has some good stuff in it. I don't know how effective it is, but I don't much care. He loves it.
One duck egg a week, if consistently given, will give a few benefits. If it's just once a month or whatever it will hardly do a thing.