Well, yes. This is a thing that works.
Yes, this works well. Chicken tractors are something that take advantage of this and use it to raise chickens in the safest (for values) way to raise chickens on pasture in a limited space. There are numerous videos on YouTube for assorted techniques, from small 20 chicken carts that are moved daily or twice daily, to massive huge trailers with hundreds of chickens that are moved less regularly.
To get the most use out of the rotational grazing (the official name of what you propose), run horses/equine, cattle/bovine, goats and sheep together (goats eat more browse/bushes and
trees and sheep eat grass and such down to the ground), then birds. You can run chickens or turkeys, throw geese in with the sheep for fun, run geese with chickens or turkeys, add ducks (if you have a wetland area you're working with), and then start all over.
Generally, give any space a good week or two, or three, between when you last run a critter on it and when you start the cycle all over, just in case there are bare patches and you need to let it regenerate for the Primary Grazers to come back.
Doing this, in this sort of order gives you a whole lot of benefits. It breaks the parasite cycle. It puts those animals that need certain types of graze at a point in the cycle where they can get it. It allows for the best sort of
land use and fertilizes the land, allows it to reset. By moving the critters frequently, you stimulate plant growth, increase fertility, and help the environment. It's fun to watch as each successive group moves through the same piece of land, finding food and adding that little bit of something that has been missing. It resets that one piece of land to the grassland prairies every major continent used to have, and how they were kept grassland prairies (minus the fires that kept succession growth from happening) and brings everything full circle in a beautiful way.
Yes, it's true that chickens don't "break up" sheep and goat piles. There's really nothing there for them to break up. If the land has been watered between the time the sheep and goats leave and the chickens start, then they will spread that manure goodness around and eat anything vaguely edible. I would suggest a good watering on the piece of land between rotations, but that's to make sure you're getting the maximum of nutritive goodness out of the
poop. You don't have to
water.
It's a good plan and I hope you move forward on it.