Our ducks live on dirt and grass but they have a large area, not a pen, and their poop does not get as concentrated that way. The rain washes most of the poop into the ground to feed the worms but I will also hose any visible poop to make sure it becomes worm food and not fly food.
The problem with using shavings is that they hold water and don't absorb poop very well. They stink so bad and create a bog in wet areas so we only use them in the chicken coops where the chicken poop sticks to them and the whole mess gets cleaned out every other week when yard waste is picked up. We don't even compost the shavings because the wet shavings smell so bad and they need moisture to decompose. It would be a huge stinky mess if we used shavings for the ducks and we would lose our awesome liquid fertilizer.
There is a difference between clean dirt and manure filled dirt. As long as I wash the dirt in high traffic areas, we are able to keep our dirt clean. The chickens have killed the grass with their thicker "hot" poop and scratching but the ducks are pretty gentle on the grass if it is hosed clean. Their poop is not hot enough to burn the grass the way chicken poop does. When we get downpours, which is most of the Winter here, the dirt becomes muddy but we have pretty good drainage so it dries up quickly once it stops raining. It is best if we can keep the ground watered because that washes the surface and puts the nitrates into the soil.
Our area does have a sandy soil and it is rocky below the topsoil for good drainage so that helps. Our rabbits live in runs with dirt over buried wire so I pressure wash their poop straight into the garden once the urine has soaked into the ground. As long as I break the pellets down, they fertilize the ground but it takes more effort than washing the duck poop below the surface. We use shavings in the covered rabbit nest boxes when we have bunnies but other than that the dirt works fine.