Would one foot be deep enough to accommodate chicken needs, i.e. scratching and dust baths, do you think?
If you were to dig 1 foot deep in area of coop.(128 sq ft coop)
It would take a man and a boy to do it. 
( you may have heard that term before

)
You are talking of moving almost 5 cubic yards of soil.
Do the math here by multiplying by 5.
How Much Does Topsoil Weigh? According to Dirt Connections, a cubic yard of topsoil weighs about 1,080 pounds. However, debris and moisture can make it heavier. Grow Your Yard states that topsoil can weigh between 1,400 and 2,000 or more pounds.Mar 23, 2021
If you only did 6 inches, it is still over 2 yards of soil to remove, and place back.
Consider this option that Bluebaby mentioned.
Get 1" X 2" welded wire. Much cheaper than Hardware Cloth. Lay flat on ground, and apply a 1" plus layer of cement on top of welded wire.
If you are not very knowledgeable about cement, I suggest these bags of mortar mix.
You may be wondering why not use concrete mix???
Answer; Concrete mix has stones that can be up to size of Quarters. Much more effort to end with a smooth finish that would not scratch/injure chickens feet. Mortar mix is cement, lime, and sand. It is easy to create a smooth finish on a thin layer application. Your 1 inch thick cement layer is not strong enough to function as a driveway for your car,,,,,,,,,,,,,,,,,,, but plenty strong enough for you to walk on.
Another option to consider are these patio blocks.
Lay them out,,,,,,, and sweep in between cracks some sand to lock then in. place. Then water down,,, and apply some more sand. Apply on top whatever you wish. Hay,, straw,, pine shavings,, sand, or combinations of whatever you wish. You will not get anything digging into your coop/run with these in place.
Hoping this gives you some ideas on how to tackle the coop floor anti digging portion.