I just saw a great YT video about chickens/gardens/compost/forage/permaculture, it was by
edible acres (all one word no spaces I think).
He was
growing stuff
in the chicken yard, protected with wire fence formed in a ring around individual plants/plots. I've also seen in another video grass/pasture/weeds grown under a moveable frame covered over by wire. In both protected systems the chickens can eat some of the outer leaves but the roots and larger portion of the plants/grass/weeds are able to keep growing. He eventually moves the protection little by little and starts seeding inside the wire ring to keep the cyle producing more.
Especially coming up in Phx area in winter I think this is a viable option for supplementing feed and keeping chickens busy/happy/employed. If you create/have a nice "microclimate" in certain areas even in cooler areas you might be able to do this. He even made a cattle panel low tunnel/greenhouse and placed it where natural drainage occurs to water it and let chickens wander thru the center aisle (side planting somewhat protected again by wire fencing).
I did something similar last spring. I used 2x4 and then put chicken wire over the top. Plants herbs for the girls. They loved it til summer came and killed it all