If you don't have any run litter at all, the run can get quite poopy and gross, and muddy when it rains. And it will freeze solid in the winter. If you are up for regular cleanings, that can help the poopiness issue, but it will still get muddy or frozen. I have a very low maintenance setup where I never clean the run, and it never gets poopy or muddy. It only ever freezes if it's exceptionally cold (single or low double digits). I have a deep layer of organic matter of different sizes and textures - wood chips, dry leaves, grass clippings from mowing, and other miscellaneous yard waste that I rake up from my yard. The nitrogen in the poop mixes with the carbon in the plant matter and forms an active compost, which the chickens stir constantly. It doesn't smell, and I don't have to clean it. The larger particles (wood chips) provide great drainage so it doesn't get muddy and there are no puddles after a rain. And, again, because of the good drainage, the top layer dries fairly quickly and doesn't freeze in the winter. The deeper layers that stay wet longer will freeze, but the top usually stays loose. I got my wood chips from a dead tree that got shredded, and all the other material is yard waste, so everything is free. I collect dry leaves in the fall and use them throughout the year. I top off the run with leaves or wood chips as needed, and throw the clippings in there every time I mow the lawn. I love this method and highly recommend it!
This is pretty much what I was about to say.
It's not technically *necessary* to have litter in the run, but a good amount of the right kind of litter solves many problems that might arise, especially odor, flies, and mud -- though no amount and no kind of litter can solve a mud problem that is caused by a fundamental drainage problem.
Like many people here, I use Deep Bedding in my coop and Deep Litter in my run. I have no issues with odor or flies, but I will admit that I'm on extremely, even excessively, well-drained soil.
We are all in different situations so what works for one or is needed for one isn't necessarily the right answer for someone else.
An excellent point to keep in mind. I rambled on at length yesterday about my decision to use straw rather than wood chips in this run. https://www.backyardchickens.com/threads/thoughts-on-bedding-litter-why-i-chose-straw-today.1481550/
Thank you for sharing! Yes, I am sort of getting tired of buying all these shavings for TSC! It is a must for my duck coop and run as they attract flies like nobodies business. But my chickens are cleaner and less stinky, and I am not sure if they directly benefit from the shavings other than it sucking up some moisture after rain. I guess I am most worried about the dirty becoming too wet and them getting bumble foot? Not sure if the two go hand and hand. This is my first time raising and having chickens. Thank you again!
Since your photos are showing woodland, you might try raking up a bunch of leaf litter to use for the run instead of shavings. I put three more gorilla carts of mixed pine straw and oak leaves plus several bushels of lawn clippings into the run this week.
Persistent wet is one of the things that can increase the chances of bumblefoot, but if your overall drainage is adequate then adding plenty of dry organic material is one of the best solutions for dampness.
Coarse material like the sort of wood chips you get from a tree trimming service is the best for drainage. I like a mix of materials better than any one sort, especially if part of that mix is leaves or straw -- which seem to be the worst about packing and matting when used alone.
@K0k0shka's point about the chickens foraging in the litter is a very good one. I never actually spread anything I dump into the run. I leave a pile and the chickens have a blast digging in it and spreading it.