Absolutely different strokes for different folks. What works best for me may not be the best for you. That's kinda why I gave my criteria, to help people think what might be best for them.
We are both discussing shredded bark, not wood chips. I think it is important to make that distinction. Those are different products with different properties. I can and do get all the wood chips I can handle free from a municipal facility. I use those for mulching trees, bushes, and landscaping beds. I don't buy or use the shredded bark.
I don't add dry den or anything else to my wood shavings. May keep my costs down a bit. With a little raking and using a droppings board, I get great results. I'm not saying you don't, just that I do.
When I clean the coop, I don't put it straight on the garden. I compost it first for two reasons. Chicken manure can be pretty strong to go straight on a garden. I'm concerned that I may burn certain plants, especially squash or cucumber type plants, if I put it straight on. I know plenty of people successfully do that but my experieces and methods may be diffeerent than theirs. The other reason is that the wood has such a low nitrogen to carbon ratio that I am concerned, if my chicken poo content is not high enough to provide enough extra nitrogen, that the wood product can draw extra nitrogen from the ground to aid its decomposition, thus not leaving enough nitrogen immediately available for my garden plants. If there is enough poo content to provide the nitrogen, it may burn the plants. I just find it less worrying to compost if first. I know this does not have a lot to do with the specific topic at hand, but I'm using it to point out that different folks do different things for different reasons.
I have not used shredded bark in my coop although I have used it as mulch in a different situation. From my experience with it, I think that the thinner wood shavings will be more absorbent. I also thing they will be easier to remove from my walk-in coop. But wahtever works for you in your specific situation is great. Go for it.