>> Is the moving-sand approach fundamentally desirable thing (I can't imagine why) or is it just a simplification for the proof of concept?
I suspect this is about operating temperatures. If you run pipes through the thermal mass then you will be slowly heating/cooling the entire mass. That means the temp will be constantly changing and would basically never be at optimum. But by withdrawing small amounts of sand to be cooled/heated separately, the bulk can remain at an optimum. Only the removed sand is cooled. So your tank of "hot" sand remains at the same temperature until the last bit of hot sand is gone, rather than it slowly cooling as you withdraw heat from the bulk. That no doubt makes thermal transfer more efficient and predictable.
I suspect this is about operating temperatures. If you run pipes through the thermal mass then you will be slowly heating/cooling the entire mass. That means the temp will be constantly changing and would basically never be at optimum. But by withdrawing small amounts of sand to be cooled/heated separately, the bulk can remain at an optimum. Only the removed sand is cooled. So your tank of "hot" sand remains at the same temperature until the last bit of hot sand is gone, rather than it slowly cooling as you withdraw heat from the bulk. That no doubt makes thermal transfer more efficient and predictable.