Yep, it's in their chicken nature to scratch and peck, and dig holes.
Sounds like you have a nice composting system set up for your aviary. The bulk of my compost run litter is indeed leaves, then grass clippings. All our kitchen scraps and leftovers get tossed into the run as well. What the chickens chose not to eat gets mixed in with the other compost litter and the worms eat it. Then the chickens dig out the worms and eat them. Good system that breaks down my compost much faster than what I could do with compost bins back a few years ago.

Have you measured the ground temp in your sand only run compared to the composted litter area? I suspect that the sand would heat up faster and retain more heat than a compost ground cover. But I don't know for sure.
Well, another advantage that I found with compost in the run is that it never smells. I used to have a sandy run (I live on a lake) but I found it too much work to keep clean. The sand always seemed to smell bad despite how often I cleaned it. My compost run smells like the forest floor. Very nice.
But as I always say, we all live in different environments and what works for me might not work as well for someone else. So, if your sandy run works for you, that's great.