If you check out edible acres chickens on YouTube, his setup is basically to take vegetable scraps, let the chickens pick through them, that composts in place, as he turns it, they eat the worms and bugs in the compost, then he gives them small amounts of organic grains from nearby farms.
I think that seems to be as close to a wild chicken diet. But I do think using chickens as garbage disposals for our food waste is the best use of that resource, meat scraps especially.