I think Shanty said it real well. It depends on your unique situation. We all have different climates, our coops look different, we have different chicken densities in our coops and runs, we manage them differently, and even have different goals. The last time I went four years without cleaning out the bottom of my big walk-in coop with fairly low chicken density, but I put a droppings board under the roosts and clean that off every two to three weeks to put in my compost pile. I dump dirty water out of my waterers but the only time I clean them is with bleach when they start turning green.
I think your original question was more about the health benefits of keeping the coop clean. My opinion on that is "what are they used to"? If you keep the coop and run spotless, they are used to that and will be really vulnerable to disease or parasites if exposed. You need to keep it clean if you keep it clean.
If they are used to the coop and run not being real clean, they will have built up immunities and can do very well in that environment. I still think you should keep the coop and run as dry as reasonable. A wet run is not a healthy run. And avoid manure build-up. Sometimes when the weather sets in wet you just can’t do much about it with some runs, but do the best you can.