That's what I do as well. I converted my chicken run into a chicken run composting system over 3 years ago and never looked back. I harvest my chicken run compost about twice a year, but I have so much compost in the run that I never use it all up. This spring, I took out over 24 cubic feet of chicken run compost for the raised garden beds and estimate that was maybe 10%, or less, of the compost ready to harvest in my chicken run.
I only clean out my chicken coop twice a year. I use deep bedding in the coop and just add fresh thin layers of litter (currently using paper shreds) maybe once or twice a month. All the old litter gets tossed into the chicken run composting system. The paper shreds compost much faster than wood chips I used to use as coop litter. I have also used dried leaves, but they can be pretty dusty. I have found, for me, that paper shreds are the best free coop litter, and they compost faster than the other litters I have used.
If you let your chicken run litter build up and compost, chances are the composting litter will be full of tasty bugs and juicy worms in no time. My chickens are outside scratching and pecking in the compost litter all day long finding stuff to eat. My commercial feed bill goes down in half in the non-snow months. I could not be happier with the decision I made to convert my chicken run into a chicken run composting system.