We have a tendency to think of clay as an entity unto itself, but it is simply another state of the breakdown of a parent material (you may know parent materials by the more common name of ROCKS

We start with a mountain. It becomes boulders which become rocks, which become sand, which becomes silts, and finally, clays. The increased surface area is what makes it so amazingly colloidal (a sponge for nutrients), but this can be a two edged sword. If there is no biology to break the bonds that bind that nutrition to the soil, it can just lock up there. We often see this with calcium, a very colloidal ion. Clay is not inherently more nutritive, but it tends to be from its nature...
The other huge issue is compaction. Clay tends towards a flake like form; think of throwing up thousand of sheets of paper high into the air. As they settle we spray with a hose. Soon we have an inpenetrable, impermeable barrier of soggy paper right? Say we find something to ball up the paper (like polysaccharide exudates from roots and bacteria) and put hoses and beams between the sheets (fungal hyphae and roots). Suddenly there are spaces in between that allow for the free exchange of gasses and air, which encourages living things, which furthers our natural release of tied up nutrition...
Suddenly clay soils are not a bad thing but a good one. We now have a soil that will retain nutrition rather than allow solubilized ions to wash away. What was once our problem now becomes a solution...
OL, exactly right about sand; it's just a raw material for more eventual clay. A temporary fix at best.
Toil, right on about the roots. They are our best claybuster we have because they encourage ALL the other factors...
and TDB, an elegant synopsis. I have waxed on about minor details, but you hit the nuts and bolts in a most thorough manner. I am SURE it was helpful, in the best traditions of this site. Nice job.

HG