What happens to the ones that don't lay enough?
In commercial operations, those chickens get turned into animal feed, typically dog food.
Won't a long cooking time fix that ?
Longer cook times let connective tissue break down and is really helpful for fatty meats with lots of connective tissue.
Older chickens don't meat this criteria, they're not any more fatty than they're younger versions, and according to google, they get tough because the muscle fibers themselves get tougher, not any more numerous.
Those used to be called "stewing hens," and were enjoyed quite regularly. You just can't cook them in the same manner as you would a young chicken. They were usually braised low-and-slow not unlike tough cuts of beef.