I started my current coop and run around 13 years ago. I do not cull, I have 2 birds from the original 6 still with me, now 13+ years old. I keep around 12 in total, replacing members that have passed the previous year with point of lay hybrids. That said...
My deep litter run is also my compost "dump", 18 to 24 inches deep, mostly leaves, grass cuttings, and wood chips.
Pretty much anything biodegradable except chocolate, avocado, and uncooked green potato skins also go in the run. Some days or weeks nothing, some days (day after Thanksgiving, or holiday celebrations) a garbage bag or 2 full of food waste, including cakes, bread, pasta, paper napkins, cardboard, paper bags, shredded mail... a bushel full of soft red bell peppers, rotisserie chicken carcasses, venison trimmings, fresh and saltwater fish trimmings, fresh killed raccoons, squirrels, opossum, etc...
If they don't eat it, they bury it. All good composting material. I don't pay attention to "treats", they get them when I get them. Last week they got a garbage bag full of stale bagels... some are still in the run. They will get another a week or so after I see none left...
Egg production does not seem to vary. They have access to 20% flock raiser, granite grit, crushed oyster shells, water, and their predator proof run 24/7.
I don't pamper or pay much attention to their eating habits. They are sulfsufficent, seem healthy, long lived, and happy.