Trees are an important part of a healthy ecosytem. The presence of trees slows soil erosion by preventing winds from blowing the topsoil away. As you know, the top couple of inches of soil are where the micobiology live. Healthy topsoil (with fungi, bacteria, organic matter, humus, protozoa) supports the rest of the web of life; smaller trees, shrubs, ferns, plants grow in.
So, when you cut down big trees, and their roots die, it compromises the soil and leaves the land open to erosion.
Without tree and plant roots to dig through the soil, how can minerals and nutrients come up from the ground and into the leaves and flowers and fruit? Without the roots, the soil gets compacted and hard. If the soil is hard, plants can't grow well. if soil is compacted, water runs off rather than going down into the soil.
I compost because I like gardening and so that's what I know about how soil is connected to healthy plants.