Honestly, you are making mountains out of molehills. This is absolutely not a case of "excessive numbers of hens in small spaces." Your neighbor has 3-4 times the recommended minimum number of square feet per hen. You're upset because her yard has no grass, but that's not "desertification" which is an actual word with an actual scientific meaning that has nothing to do with manual removal of the sod. Scratching up the grass is chickens doing what chickens do. The soil is not damaged. Were your neighbor to get rid of the chickens and till and plant grass, the grass would grow like crazy.BTW I grew up in a family that always had 8-12 chickens. But we also had several acres for them to wander around on. So although I'm somewhat familiar with chickens, I was pretty ignorant about situations in which urban people have excessive numbers of hens in small spaces for some reason.
My neighbor is an urban person: to her, desertification & a small crowded yard seems normal & reasonable.
This has nothing to do with aesthetics. I wasn't growing anything but weedy grass in the areas they are in. But I am protective of soil, e.g. when I garden, I rarely leave soil exposed for longer than absolutely necessary so as not to expose it to the oxidizing effect of sunshine.
It's going to take an awfully long time for eight chickens to build up nutrient levels to the point that the yard won't support plant life. Heck, your other neighbors that use Miracle Grow and ChemLawn are putting far more phosphorous and other nutrients down than these chickens. Manures of all kinds are actually low in nutrients compared to the fertilizers people buy. The nitrogen in the droppings is unstable anyway--N has to be reapplied every year because it breaks down over time. Heck, I have a part of my property that has been soil tested at *5000 TIMES* the recommended amount of phosphorous because long ago there used to be a feedlot there--stuff in that area grows like crazy--the only thing the high P means is that I don't have to purchase and apply phosphorous there ever. Your town does not have a three chicken limit for environmental reasons, they have a chicken limit for social reasons. They think three chickens are enough for the chickens to have a flock and keep their little chicken sanity, but it's not enough birds to annoy the neighbors.
There is absolutely nothing, I repeat, NOTHING that sunshine will do to soil. There is no oxidizing effect. Crop residue is left on the soil to prevent wind and water erosion, nothing more. Cover crops are planted to prevent erosion and to add humus to the soil. The "oxidizing effect" simply doesn't exist.
I am not trying to be rude, but you seem very ignorant of environmental science, soil science and animal husbandry. And if you need my credentials, I was an environmental science educator for 13 years, have taken soil science classes and helped FFA kids with soil science projects, and am a certified University Master Gardener. My Master Gardener classes included college level soil science.
As I said above, your neighbor is doing absolutely nothing wrong. It sounds like she has happy, healthy hens in uncrowded conditions.