I view my responsibility to put aside my personal views, agendas, campaings and give what I consider the most balanced advice given the information I have from the OP's question.Note that your comment that hens will still lay eggs on some truly terrible diets applies to commercial feed too.
The key thing a commercial feed does is satisfy AVERAGE requirements (optimal, I think not). So most individuals are actually poorly served by it because they are not, in fact, average. The free choice feeding research shows that not only is it better for the health of the animals, but it is even more efficient for the pocket of the person buying the feed, if the animals are allowed to select their own ration.
The papers on this for chickens were given in the thread on new research debunks trad advice, and here's a paper that shows it for cattle too https://practicalfarmers.b-cdn.net/wp-content/uploads/2018/10/Atwood-et-al-2001-tmr-vs-choice.pdf
As both you and I have discovered through experience, feeding an alternative diet isn't quite as straightforward as it initially seemed. Both you and I have made quite considerable changes to our feeds over time; your first and second articles for examples and my posting on my thread.
https://www.backyardchickens.com/ar...eat-tears-a-calculator-or-deep-pockets.78655/
https://www.backyardchickens.com/articles/wholesome-homemade-feed-2.79307/
As examples, I wondered why the chickens I care for craved bread and I finally worked out that the diet I fed them was low in salt and it was the salt in the bread the chickens were after. Fermented wheat and peas didn't work for me or the chickens and a further complication is the chickens diet choices change thrughout the year; availability is one reason but also the need for other nutrients depending on their state of health and time of year.
If one has a wide variety of plants and bugs such as you have in your garden it's probable the chicken can find what it needs. Not many people have such a range of food options. Another factor is free range on a quarter acre plot mostly covered in grass is nothing like the same as free range on mutiple acres of mixed vegitation.
It's not that alternative feeds won't work but to work well there are other factors such as available forage, time out of coop and run, quality of the forage etc etc.
I would also point out there are no long term (hatch to death) studies on the effect of a particular alternative feeding regime.
There are numerous fad feeding regimes on the internet for both people and chickens, very few of which are based on any long term evidence.
My view is anyone who posts on BYC questions about these alternative feeding regimes has not done sufficient research, or the calculations necessary to undertake such a venture and any advice given should bear this in mind.