I've got a book written by a scientist from Utah named John A. Widtsoe around the turn of the century called "Dry-Farming : a System of Agriculture for Countries under a Low Rainfall". (He was also a high ranking official in the LDS church, so if you look up his writings you will see both scientific and religious writings. It isn't a mistake, you have the right guy). He did a lot of research on desert soils and came to the conclusion that the common model of three layers of soil (topsoil, subsoil and bedrock) was not appropriate for desert soils. He decided that the model was developed in well watered areas like Germany or the eastern half of the US. He didn't observe the differentiation in desert soils described in the classic model, but found that their fertility extended quite deep. My thumbnail summary of his book is that the humus in the topsoil is necessary to hold the nutrients in areas of abundant rainfall, but that lack of humus in the desert is less of a problem because it isn't subject to anywhere near the same amount of
water dissolving and removing nutrients. Of
course, there is a lot more than that in the book, but I read the book quite a while ago and that was my take away.
If this is true, it doesn't mean adding humus to desert soil is a bad thing (if nothing else, humus on top of the soil will prevent drying out, but it does provide a possible reason why desert soils, which are often very low in humus are still very fertile. Also, humus still is a great help in holding water in the soil.
Before we throw out the baby with the bathwater, maybe we need to reexamine the use of fire. It was the most used method of ecosystem adjustment in the new world, and while they were a stone age society, they were a pretty savvy stone aged society and developed some pretty cool systems and crops. Small, low intensity fires are less likely to burn to ash, leaving a lot more plant detritus and such fires are less likely to open an area up to much erosion, especially if the fires are timed so that there is enough moisture to sustain an immediate weed bloom of edible weeds.
My wife's uncle grew up around Yosemite National Park back in the 30s and 40s. At that time he said he watched the
local indians burning off fields for their oak trees. He said they would pick a cool, dampish foggy kind of morning in the spring and move with the fire, protecting the plants they wanted to not disturb and pulling up or otherwise destroying the ones they didn't want. In such a case, you will loose some
carbon, but there won't be much erosion and if it results in a big weed growth (from weed seeds in the soil seed bank waiting for a fire to sprout) the resulting weed growth may deposit a lot more plant material than was burned.
(I'm just suggesting this as a possible scenario, I not emotionally invested, so if you see a flaw in my proposition, you may proceed to mercilessly rip it apart with the knowledge that it won't bother me, much.)