I have DL in coop and run. My run is mostly NOT covered. We've been having record wet weather. Yes, the DL is sopping wet now. But, no matter what was in the run at this time, be it grass, sand, or DL, it would be soaked unless my entire run was covered and any breezes would be prevented from blowing through the run.
Wet happens. A good DL has a variety of materials. Naturally, the finer materials will sift down to the bottom of the matrix, while the looser materials will stay at the top. Just like in a forest floor. Shortly after a rain storm, if you go into the forest, you will find that the loose material laying at the top is actually quite dry. But, if you dig down a bit, you will find that the underlying material is damp, like a sponge.
That's what DL does. It grabs and holds that moisture to prevent either extreme: too wet or too dry.
A bare soil run, in a sudden monsoon deluge will turn into a mud pit, with rivers of fecal laden water running off to contaminate the surrounding ground. While a little nutrition is a good thing, too much N and P (uncomposted manure) is an environmental pollutant.
I am convinced that bare soil is NOT a healthy state. God designed things differently. If you observe the world around us, you will rarely see naked soil unless man has made it so. After a wild fire, weeds quickly spring up to cover and protect the soil. In a forest, the litter is constantly being renewed by the tree canopy and the understory plants. The tilling practices of the grain belt have given rise to erosion of FEET (not inches) of top soil, as that area marches towards desertification.
The following paragraph may seem like a totally unrelated topic, BUT... it is one more example pertaining to the benefit of keeping the soil covered.
I have been doing deep mulch in my gardening practices for the past 40 years. Even without use of cold frames or other climate enhancement, my garden grows produce earlier and later in the season (by at least a month on the front end, and at least 2 - 4 weeks on the back end of the season.) My soil is loose and friable while the soil of my neighbors is still frozen, or so wet and compacted that they can't work the soil.