Sunflower, it must depend on soil structure but I have gotten along fine with subterranean and semi-subterranean composting for the last 5 years. Before that, I was doing about 50:50, semi-sub and bin composting.
My soil is gravelly, about the best way to describe it - glacial till. It drains well and probably holds a lot of air once it is disturbed.
In the fall, I dig out several beds to the depth of a shovel, toss all the frost killed plants in there and recover for the winter. It only takes a little raking in the spring to ready those beds for planting. Composting-in-place.
Most of my composting is done in a 4' by 10' bed that is never planted. I have been able to just keep some compost and some soil covering the compostables that show up almost daily. As I work my way from one end to the other, what I put in earliest becomes available for garden use. It is extremely "hungry" and everything decomposes quickly!
Finally, I have 2 small wood decks - one outside my backyard chicken coop and the other outside the greenhouse. These are small enough so as to be movable. Under them is my "stealth" composting. Once again, they are dug to about 8" and the compostables are covered until decayed.
There is no actual compost pile (or bin) anywhere but lots of composting going on.
We are each other's harvest; we are each other's business; we are each other's magnitude and bond. ~ Gwendolyn Brooks