Nutrition is a factor for all hens surely. While premature ageing is a problem for egg production hens (among many other conditions).
After I wrecked one of the hen's liver with bad diet, the vet told me 'good nutrition' is a mix of high protein pellets and forage. (Sorry to keep referring to him, I work fulltime and have limited capacity to consult the literature, whereas he's an avian specialist. The hen with fatty liver lives on rambunctiously thank to his advice and also a tiny thanks to me for sticking to his advice for a couple of years now. Her diet includes a few added supplements that can be low in pellets and forage.)
@Iluveggers mentions treats. There's a big difference between handfuls of mealworms (which are quite fatty) and something like kale. If treats are chosen wisely it seems to me there's no cause for concern.
I think and everything I've read on any species, including our own, is a varied and balanced diet combined with exercise is likely to promote physical and mental health. I've never seen any reason to argue with this. Zoo animals have from what I've read fared better in wildlife parks than they did in cages in zoos.
Of course, in the wildlife parks in the Northern Hemisphere these species need to be fed in most cases. I know types of commercial feed are available for these species. I even knew someone who specialised in them.
I've always free ranged partly on principle and partly on my experience that free range chickens are less prone to some of the stress problems associated with those fully confined.
I've never fed chickens just commercial feed and nor has anyone else I know.
I agree with Perris that commercial feed was developed to provide the most basic nutrition at the lowest cost giving maximum egg yield. I have never read anything that suggested any of these feeds were designed for a healthier and longer life for the chicken.
Again, the chickens that I've known since the 70's tended to live longer if they survived predation than the impression I get from reading these forums of the current heritage and production breeds.
So for me the feeding isn't ever likely to be an issue. Even if I can't fully free range chickens I will always ensure they get time out of the coop and run and get fed other things to provide variety in their diet.
One point of interest and perhaps a point of reference is there were most years between 20 and 30 chickens of mixed ages and sex in Catalonia. A 20kg bag of commercial feed lasted on average 25 days.
At the allotments there are now 20 chickens of mixed ages and breeds, plus one male and they get through 3x20kg bags a month.