Dilbert. You are absolutely right that is what I found out.
The labs do test soil with a settling test for percentages of sand, silt, and clay.
If a soil test is properly taken, there should not be that much organic matter in it. the soil should be taken from the root zone 3-7 inches deep to exclude mulch and whatever just sits on the surface of the soil.
Particle size does matter when adding sand to clay soils. It would probably also be costly. Not any sand will do, it has to be large particle coarse sand and 50%-75% by volume of the soil would need to be added. Insufficient amounts of sand would take up the air space and the soil would be akin to cement.
Interesting though, cinders are not that bad to add to the soil as long as you don't walk on it. It helps with drainage and aeration because the particles are large, porous, and they are a source of minerals. Rock dust can be made from crushed basalt. Black cinders are lava rock cinders.
I have successfully grown orchids, anthuriums and citrus trees in black cinders for years. One of my citrus trees has been in the same pot of cinders for 14 years. I have found that the secret to longevity of plants in pots is aeration. Cinders do that very well.
I also know that ideal soil is 5% organic 45% mineral (sand/silt/clay), 25% air 25% water.
The ratio's are important. The composition of the mineral part of the soil determines in the most part pH, how well the soil utilizes nutrients and holds or drains water. Most of the minerals that plants need come from the minerals stored in the soil.
Plants can live without soil if nutrients, air, water and root anchorage are provided.
However, most plants cannot survive in pure organic matter very long. They need access to the minerals, support, and balance that the soil provides. That is why organic matter is worked into the top few inches of the soil, but the roots of the plant will go down deeper into the soil layers if air, water, and nutrients are available.
If that soil layer is poorly drained, lacks air spaces or is impervious to water and roots, most plants will start to show signs of trouble when the roots get there.