I've successfully free ranged for many years without predation problems. I use farm dogs for protection of the livestock and I keep a rooster in the flock at all times. Both are effective predator deterrents. I never close the pop door and my coop is not a bit predator proof. I do not have a stationary run of any kind.
Over the years I've only lost one rogue loner hen to a Great Horned Owl when the hen refused to roost in the coop. Three chicks were lost to a black snake when they were still confined to the brooder pen, but applied moth balls around the coop and never lost another in this fashion.
The benefits to free ranging are myriad...fresh, healthy soils underfoot, no parasite cycling, better overall health, fresh and natural proteins and green forage, exercise, a more natural existence, a better chance of escaping predation than if confined to a pen...it's like shooting fish in a barrel to keep chickens confined to a pen that predators can breech. Out in the open they have a better chance of evading these predations and the dog can actually get to the predator out in the open.
Right off hand I cannot think of the advantages of keeping chickens in a stationary run.