Three generations of women raising chickens here and I can honestly say we've never had an egg eater...we've had hundreds of 'em. IMO, there is no such thing as an "egg eater" or we would have eventually run across one in our flocks. ANY chicken will be an opportunistic egg eater, meaning they will consume a cracked, leaking egg in the nest, on the floor, etc. That is not only natural but necessary, if you think in terms of this bird species living in the wild.
A broody will even push out non-fertile eggs and eat them, but to lay an egg and turn around and eat it...no. A bird that did that would have no opportunity of passing on the gene and its line would soon die out, in a natural setting.
The problem is thin shells or even too many eggs in one nest that get crushed when hens climb in and out...but usually it is thin shells. It isn't caused by folks feeding their chickens egg shells or broken eggs, creating a taste for eggs.
You can't "cure" it by planting loaded eggs or fake eggs. The only cure is creating stronger egg shells. Sometimes this just comes eventually as the birds are once again diverting calcium into eggs instead of feather regrowth. Or you had a chicken that was experiencing temporary calcium depletion and she only laid a series of thin shelled eggs but resumed her normal shell strength and magically, it seems, the egg eating stops.
Whatever the original cause, the most expedient way to correct thin shells is placing more calcium right in your feed ration and making sure they have plenty of protein in their regular ration. If you currently offer free choice OS, mix some right in the feed. If you don't offer any at all, do so. Try to see if your birds are eating more layer ration vs. "treats", if not, cool it on the scratch and treats.
If you say you never see any thin shelled eggs but you see yolk on the others or on a chicken's beak/face, it could be the thin ones are being consumed before you ever find them. If you have a sudden drop in egg production, see egg residue on the eggs or nest or on a chicken's guilty mug...before you assume you have a cull bird, just try upping the calcium and protein and wait it out. Things will correct themselves 9 times out of 10 and you won't have to kill that nasty bird with a taste for eggs....trust me, they ALL love the taste of eggs.
And that's just my take on it....