As a general rule, and subject to knowledgeable adjustment by people who have done research and backed it with experience,
Chickens other than Cornish X broilers should be free-fed with a quality commercial feed -- available at all times and as much as they choose to eat.
As
@U_Stormcrow has so ably explained, forage varies wildly in abundance and quality thus cannot be depended on too greatly -- especially for modern, high-production breeds (you may not think of your birds as "high production" but the Brahma in my avatar, the worst layer in my flock, laid more eggs in her first year of production than a Leghorn would have been expected to produce 100 years ago).
It's important to note that the defining characteristic of layer feed is that it was developed as the cheapest formula to keep confined commercial layers in production for the single year of their laying life, not to provide a long-term optimal diet for a dual purpose bird in good health for multiple years in a backyard setting.
Adding scratch grain to that already iffy diet dilutes the nutrition further.
Many of us here prefer to use an all flock type feed with at least 18, preferably 20% protein to better support our larger birds over their longer lifespans and then offer oystershell on the side for the laying hens' calcium needs.