Agree 100% that it is tough and potentially inadvisable unless you live in a warm climate and have significant space for piles and forage.
Also, it is “in process” compost that would provide nutrition, not finished compost.
That being said, an appropriately sized, active pile can significantly reduce use of commercial feed.
I do this actively...I always have layer pellet available, but when the weather is cooperating and I’m getting lots of compost inputs, I see intake in commercial feed go down from 50-75%.
I hope to get out today for a load of food waste today, actually.