Soil structure is not automatically present in compost or soil. It comes over time from not disturbing the ground. The soil you build on top of has existing structure, and the new compost will not. But the longer the compost sits undisturbed, the more structure it will gain. Soil structure is formed by fungus, animals, and microbes rearranging the particles in the ground. Digging interrupts that and makes the process begin again. Soil structure can act as conduits for roots to grow through and find nutrients.
These same organisms that make soil structure are also breaking things down and releasing nutrients to the plants. This includes the organic matter in the compost and mineral rocks in the soil. The organic matter breaks down and releases its nutrients faster than the rocks release their minerals, but they are both continually breaking down. The minerals in the soil are becoming more available, just at a much slower rate than the compost is. Finely milling it with a machine slightly speeds this process up, some organic fertilizers are just ground up rock. Some synthetic fertilizers take this rock and treat it with acids to break it down into pure molecules that are quickly available.
The undisturbed soil isn’t bad or unavailable. Think of it as a reservoir.