One thing I''m wondering is...why do chickens tear up plant roots?
I'm thinking they are much more interested in looking for bugs to eat than eating plants, so they root up all the plants looking for bugs.
I agree that they want the bugs and I guess they just can't help themselves from tearing up the plant roots. But, I know they love the plants, too. I guess it might be the one chicken "design-flaw" that they destroy one thing they want to get to something else they also want.
I try to assist in their efforts by putting a lot of autumn leaves in the run. That encourages the leaf eating bugs, worms, and critters to make themselves available and gives the girls something to scratch through. It also helps when it rains and rebuilds what soil the girls leave behind. I "mow" the leaves with a lawnmower that has a bagger and then throw them in the run - easy! They're partially chopped that way and the chickens have a blast!