So basically cover cropping reduces erosion?

This is pretty well known. It also builds organic matter and reduces fertilizer needs by bringing up and facilitating nutrients by acting as green manure. Even better if you can graze it before planting the cash crop, if you don’t end up doing damage by going into a field with livestock when it’s too wet. But late fall grazing, or winter grazing when there isn’t much snow can accomplish the same without compaction damage, if you don’t hit it so hard that it doesn’t recover for spring. With rye, that means before it starts heading out in late season.