the only thing I can think of is they won't have access to the dirt and the yummy to them bugs that live in the dirt. At least they will have some fresh greens. I would just make the wire so you can remove it if need be for planting or if you just want to let them scratch around in the dirt for worms. Either way you can rotate which planter boxes they are allowed to get into.
One of my black sex links almost sits on my shovel if I'm digging because she knows I'll dig up worms. LOL She throws a fit when I'm digging in the garden and she can't get in there with me. Last time I ate any worms was when I was in the military and they didn't taste that good to me. ha ha
One idea I had for attracting bugs for them to snack on is to stack and nail boards and leave a small gap (like 1/4") between the boards then place it in the run. Those yummy bugs like dark, tight, moist areas to crawl around in and they love to hide under wood. Free high protein food!