Believe me, I went through that process for 6 worlds in a row now, I know all about the tediousness of it all
I was thinking more along the lines of having them available at qualities up to a certain point. Kind of reverse of the minimum quality that other animals have. That way, you'd still have a "good spot" to look for ok quality chickens and reason enough to actually check their quality when outdoors. The whole point was actually that - diversity of action when encountering chickens in the wild.
Somewhere along the line of up to q40 was what I was thinking.
OR they could always just make a separate entity between a wild and domesticated chicken and allow the quality on wild ones but make them q10 after domestication, like all other tameable animals. Taming would be time spent in a coop or something like that.