I live on a lake, and we have hawks and Bald Eagles overhead all the time. I cannot let my chickens free range. So, I bring the free range to them in their bird netting covered chicken run. I bag all my grass clippings and throw that and just about anything else organic into the chicken run. In the fall, I mow up and dump all the leaves in the yard into the chicken run. Last fall I measured about 18 inches deep of litter in my chicken run composting system. It is full of good bugs and worms to eat. Like you, my chickens prefer to forage for food before eating their commercial feed.
My commercial feed consumption goes down by half or more during the summer/non-snow months when my chickens are outside foraging in the chicken run compost system. I personally think the eggs are better when the chickens have access to all the compost in the run. The yolks of the eggs are just a darker orange. But I still keep their commercial feed available 24/7 along with extra grit and calcium in separate small PVC feeders. The grit and calcium do get eaten, but for my 10 chickens, it takes maybe 2-3 months before refilling.