My hens spend most of their day is a large roofed pen (10' by 30'). This keeps them safe from dogs, hawks, and mongooses. It means that I can find the eggs in the nest boxes rather than under bushes helter-skelter around the farm. The pen protects them from bad weather. It allows me to harvest manure for the compost bins. The hens run free to scavenge bugs and lizards in the late afternoon for a few hours when it is relatively safe. I'm usually working in the area and can keep an eye out for predators. If they ran loose all day instead of being penned, then their poo would be on the ground someplace around the farm instead of under a perch, in a nestbox, or on the pen litter. Plus the hens would be in danger of being killed by predators. They'd still be poo-ing, but it wouldn't be as noticeable.....except for on the bottom of one's shoes. Yup, I'd be sure to step in it. By the way, I have feral turkeys and pheasants that visit the farm daily, leaving poo piles behind. I have to keep a diligent eye out to avoid piles.
Yes, chickens can be "dirty". Animals poo and that's a fact of life. It's not something that upsets or worries me. Unlike some commercial farms, my birds are healthy, have no parasites, nor harbor dangerous pathogens that I am aware of. I don't fear working around my flock. I don't mind them being chickens and dirty-ing up the place. Besides, their manure is valuable.
If one considers poo to be toxic waste, then farming livestock surely isn't for you.