When you look back at history as far as food production, it is important to remember a lot of people went hungry during different times of the year, and some years were much better than others. As man did more interventions, food became more consistently available, all year long, and every year.
However, I too have played with this idea. A couple of discoveries I have made.
* bugs are available here only about 3 months out of the year. During the height of summer, my hens will eat less commercial feed. Mine are good foragers, love scratching, and would probably survive without as much feed, but the laying would suffer. In the old days, eggs were very difficult to come by at different times of the year.
* Keep the age of your flock young, I have heard otherwise, but right now I have 2 three year olds, that are not laying at all. Young hens tend to lay through out the winter.... better. And are laying well now. Maybe there eggs are a bit smaller, but they have them nearly every day.
* Mine free range in all the acres that they want - there is no fence to keep them close by, but they tend to stay fairly close to their coop. We live on a ranch, and have no close neighbors.
* I have a rooster, and I think it does help. I have raised chicks with a broody hen for the last three years, and will hopefully never have to go back to buying chicks or hatching eggs any other way. However, I have bought chicks to slip under a broody hen at hatching time, to add some different breeds to my flock.
* Lots of chickens cost lots of money. I have found that for my family, 6-10 hens is almost perfect. But that would depend on the number in your family.
I have kept chickens for the last 5 years continuously, and at different times before that. I hope you consider this a contribution to this idea.
MrsK