Compost is not just decayed organic matter. Composting is applied microbiology at its most complex, involving the interactions of thousands upon thousands of different species of microorganisms (2 million individuals per gram) in a highly complex ecosystem. The composting process kills weed seeds and human and plant pathogens; that doesn't happen when leaves and other detritus rot down on their own.
Once applied, compost "balances" the soil flora: that is, for each of the scores or more of disease organisms that can affect each species of plant, at least 12 to 15 different species of bio-control microorganisms need to be present, with the food and conditions they require, if the plant is to be healthy. Composting accomplishes that, among other things.
The same soil tranformed, after a very light composting and a sweet potato crop (shared with a family of bandicoots, but there was plenty for everyone)
For more about soil microorganisms and the vital role they play, see "The Living Soil: Importance of Soil Organisms" in the Sustainable Soil Management Soil System Guide by the Appropriate Technology Transfer for Rural Areas (ATTRA) in the US: ATTRA
"One of the major benefits bacteria provide for plants is in helping them take up nutrients. Some species release nitrogen, sulfur, phosphorus, and trace elements from organic matter. Others break down soil minerals and release potassium, phosphorus, magnesium, calcium and iron. Still other species make and release natural plant growth hormones, which stimulate root growth.
"A few species of bacteria fix nitrogen in the roots of legumes while others fix nitrogen independently of plant association. Bacteria are responsible for converting nitrogen from ammonium to nitrate and back again depending on certain soil conditions. Other benefits to plants provided by various species of bacteria include increasing the solubility of nutrients, improving soil structure, fighting root diseases, and detoxifying the soil."
Other soil organisms: earthworms, arthropods, fungi, actinomycetes, algae, protozoa, nematodes (mostly beneficial): "All these organisms -- from the tiny bacteria up to the large earthworms and insects -- interact with one another in a multitude of ways in a whole soil ecosystem." Total weight of soil organisms per acre of healthy topsoil: about 4 tons.
Real composting has been a scientific process since the 1930s. In fact it's nothing new -- the Spanish Arabs were master composters, and Chinese peasants have composted virtually everything for centuries. But science has made it a simple matter --