I don't doubt the ability of chickens -- at least of game-type and landrace birds -- to balance their own nutrition in a sufficiently-rich and varied environment when given space enough to never run short and/or a sufficient supply of the minimally-processed feed ingredients that the birds never have to compete for them. Especially when kept on this regime for a number of generations to naturally cull out birds that don't balance their intake.
You might be interested in a little experiment I started last year.
I let 3 hens that went broody raise clutches. The first clutch, June hatch, consisted of 6 purchased hatching eggs (bought from a reliable source I've used before to bring in some new genes) and 2 home grown. Only 3 hatched, 2 out of the 6 purchased and 1 out of the 2 home grown, the rest were infertile. This was very disappointing compared with previous years. I don't know why fertility rates were so poor, but was glad I had a mix of purchased and home grown and that they performed similarly, because it suggested that whatever the problem, it wasn't just me.
The second clutch, July hatch, consisted of 8 home grown eggs. All hatched, but the chick in the largest and freshest egg set did not manage to extract itself from the shell before the broody abandoned it and brought the rest out.
The third clutch, August hatch, consisted of 6 home grown eggs. 2 hatched. One had died about day 19, the other 3 were infertile.
So the fertility rate was quite erratic; I don't know why.
The experiment started as soon as they hatched. None of these 12 chicks has eaten any commercial feed, ever. I gave them chick-feed as described in old poultry manuals, from an age when commercial feed did not exist, and their broodies took them foraging from the moment they exited the nest. Nor have they been medicated, ever.
One - one of the two purchased eggs - died at 4.5 months old, cause unknown. The rest, 11 out of 12, have made it to adulthood. And that's free-ranging with dogs and hawks around, as well as eating a concentrate-free diet.
All the 8 pullets have started laying, with no issues bar one shell-less egg and a couple of thin-shelled ones when one or two of them were coming into lay. The three cockerels have taken their place below the dom and help him look after the hens and pullets.
I am looking forward with interest to see if fertility rates are better this year.