Not to answer the question absolutely, but to give a structure for thinking about it; I'd say that soil storage of heat involves three factors: the heat capacity of the soil (how much thermal energy can be stored per unit of mass), the heat conductivity (how quickly heat will move through a given area of soil under the influence of a temperature difference), and the heat transfer efficiency - how heat in one medium moves to another at a different temperature. The first two properties depend a great deal on the moisture content because water has a relatively high heat capacity and also a high heat conductivity. When one "charges" the heat storage volume with warm air circulation, one may indeed raise the temperature, but also deplete moisture. Thereafter, recovering that heat may be quite less efficient.
If the soil heat conductivity is low due to low moisture, then it is relatively difficult to extract heat - a more intimate contact between soil and piping is needed, so the pipe system becomes quite expensive in one way or another. And of course, this piping is buried and inaccessible. Blowing sometimes warm and sometimes cool air through the pipes may give rise to issues of condensation in the pipes, and associated corrosion. Corrosion is the enemy of good heat transfer because while metal conducts heat well, metal oxides generally do not. Industrial heat exchanger equipment is regularly maintained by various means of cleaning to prevent the accumulation of "scale" or "fouling" on heat exchange tubing.
I have heard of people building Wofatis with "earth storage", but it has always sounded like one of those things that seems good in theory but difficult to achieve. If a wofati design is working well, it is because the earth is serving as good insulation. If it is good insulation, it is poor heat storage. Better to provide some buried water mass for the heat storage than to depend on soil, imho