Mulch acts as a protective layer for any garden bed, protecting it not only from heat and cold but also the weight of water and footsteps. Heavy rain will compact unprotected soil and ruin its composition. Direct weight on soil from human or animal footsteps--especially on already wet soil--drastically compacts and hardens soil. A layer of compost protects the compost from compaction by both rainwater and direct weight. In this manner, mulch doesn't soften dirt but prevents soil from hardening and compacting further.
As mulch decomposes in a garden bed, it provides a layer of light, loamy organic matter. In time this matter mixes with the rest of your garden soil. Over the course of a few years of regular mulching, a garden bed's soil composition will soften drastically as a result of this fresh organic matter.
Mulch is especially effective at softening compacted clay soils. As organic mulch decomposes into clay soils, its large particles mix with the small particles that make up clay soil, aerating the clay with oxygen. A much softer loamy soil is created that is both easier to work with and healthier for most typical garden plants.
Organic mulch provides food for the many beneficial microorganisms that thrive in healthy soil. These organisms--from worms to infinitely smaller creatures--excrete a sticky substance that is important for bonding soil in large particles and providing a more granular, softly textured soil.