Consider the following. The subsurface portion of the typical tree is about equal in overall mass to the aerial portion. So, when we excavate this mass, we are essentially removing a great deal of biomass from the orchard soil. If we were to assume a 14″dbh tree might give us a cubic yard or better of organic matter from the root system, and at an average cost of 30$ per yard (ie wood mulch) we are sacrificing 30$ per tree in organic material. Also consider there is no practical procedure for putting organic materials that deep into the soil, and if we could it would destroy the soil structure if we could. Furthermore, the heavy equiptment necessary for stumping would compact the soil at the same time it is wreaking havoc with the soil matrix. Compound that with the petroleum needed to do the work (in terms of environmental impact), and the cost of the work in dollars. Lastly, we are left with an enormous mass of root and stump of which volumes have been written about regarding the rigors of its eradication.
The alternative approach instead sees the now deceasing root system as a blessing. Although it will take years to degrade, there is no rush in the orchard. It will create an improved soil structure, with higher organic content, air and water penetration, and drought suppression. Furthermore it adds nutrients, short and simple. While any carbon rich material temporarily ties up nitrogen in the soil, the intact structure of the bulk of the material will only do this incrementally since the decay will occur mainly at the soil/wood interface. When the fungi and microorganisms have completed its transition to humus, nitrogen and other nutrients will become available to the crop. Oh, and for free.