As is almost always the case the keeping circumstances are a major consideration. In Catalonia for example a chicken with one leg wouldn't be able to keep up with their tribe and would, in a fairly short time, be picked off by a predator. Is it better knowing this to euthanize the bird or let the predators do a not so quick job later?
I've found birds so badly injured but still alive, just, that I knew there was no way they would ever recover to a state where they could free range. I can't see having a bird contained in a coop and run while their friends and family wander a satisfactory solution.

Broken legs were one of things my vet Gloria in Catalonia would not try to fix. In her opinion the suffering and often doubtfull outcome made an attempt an act of cruelty. I had one hen hit by a Goshawk. She took a full weight strike to her back. I didn't appreciate the severity of her internal injuries and kept her alive for eleven days after which she died. I still regret the suffering I put her through when the kindest thing to do was give her a swift death.
On the other hand I've had chickens with horrendous looking flesh injuries who one wouldn't think would survive another hour, let alone heal and make a full recovery.
Sickness is always difficult, especially if one isn't sure what the sickness is. Again I've had chickens looking as if they were at deaths door one day and a few days later show marked signs of recovery.
I've had paralyzed hens who took weeks to recover with a lot of supportive care that many people would have killed believing they were doing the right thing.
I can't find it in me to condem people who euthanzie their birds for their own sake or the birds. I've found sick and injured chickens to be extremely stressfull at times, more so than the stress situations that are in the top ten list for humans.
I've seen more chickens die than the total number of chickens the regular contributors of this thread keep combined. At my uncles farm we used to kill a couple of hundred in a day. I was young and they were killed for eating and I helped. I would still kill chickens I've raised to eat and have done so in the past.
These last two years alone I've had a dozen or more birds die. That's twice the number of many peoples tribes.
I can care for Ex Battery hens because of the experiences mentioned above and still make emotional attachments to/with them. For many people the combined horror of knowing the lives Ex Battery hens had and finding they die just when one thinks they are begining to enjoy their horribly short lives is just too heart rending to manage.
This is in part why I believe caring for Ex Battery hens is what I should be doing, because I can.
I would love a tribe of Light Sussex or Dorkings but they don't need what I hope I can give to the Ex Battery hens day after day, arrivals after arrivals and death after death.