For people who TRUELY need eggs for food, we'll give them away or give away extra meaties that we processed. However, those people, so many of them don't want to take something for nothing. Even if they can only manage a dime for 2 dozen eggs, they want to pay something or do work to make up for it. Heck, when we moved, we gave a couple with 4 little boys 4 hens and a coop/run so they could keep getting eggs and I know those hens are highly productive egg layers who eat very little. Our neighbor who kept other hens drops off food/supplies monthly still. Those people are trying their best to better themselves and their children, so that's who deserves cheap/free healthy food.
If people can afford the eggs and want them free, nope, no how. Right now, I can sell for less than even the grocery store standard "icky" eggs, so you can pay for the eggs from me or you can pay more at the store, but my chickens aren't free, so their eggs aren't either.