WHAT??? If you have just a few hens you want to keep for pets, you can afford to keep them until they die at a ripe old age. I have done that on occasion. If the purpose of your flock is to produce eggs for your family, you cannot. After about three years or so, egg production declines dramatically, and at that point my old hens ended up in the crock pot. In the natural world, very few animals die in their beds of old age. Sooner or later, almost all of them end up as somebody's dinner. My hens were all well fed and well cared for (which would not be the case if they were running around in the wild) until the day they ended up as mine. You just can't beat an old fat hen for chicken and dumplings. Sorry.
Where did that "lose nutrition" nonsense come from? Laying hens are bred to produce eggs and layer feed is made to help them do it. As for taking a sick hen to the vet, first of all, most vets do not treat chickens, secondly, spending several hundred dollars to treat a four dollar chicken just isn't practical, and thirdly, chances are that whatever is wrong can't be fixed anyway.
Although my Cornish X lived a relatively short life they did not suffer. They ate, grew, and made happy chicken noises. They looked and sounded content. In other words, they had a great life except for one very bad day minute.