The book I read about how chickens shaped society doesn't address that point directly, but indirectly supports that theory. Chickens were bred initially for fighting and for religious purposes (and in many cases those were sort of co-mingled purposes).I recently read Gail Damerow's guide to raising chickens ( which I definitely should have been reading before getting them, not after). She discusses how breeders chose to emphasize either esthetics, productivity, or longevity when developing a particular strain. I was quite surprised by her statement that the breeders who had constantly put longevity and hardiness as their first goal, were the one who raised game birds.
She also says this isn't so true nowadays as cockfighting is strictly forbidden (fortunately I would say but I'm not clear that's her point of view) so they are now bred for showing and esthetics.
The key thing about cockfighting was in many cases to have a rooster that was a 'winner' and then kept for stud as it were. Prices of a winners offspring being very high. So in that case you would want at least the males to be long lived.