First, a correction: savanna is not a desert. It's a tropical/subtropical grassland with scattered trees—distinct biome, distinct climate, distinct ecology.
Desert: <250 mm rain, sparse/no trees, bare soil dominant.
Savanna: >500 mm rain, continuous grass layer, tree canopy 5–30%.
Transition: Sahel (desert → savanna), Chaco (dry forest ↔ savanna).
Dry-season fires (natural + human) maintain grass dominance, suppress woody encroachment, recycle nutrients. Trees adapt: thick bark, underground organs, resprouting. Without fire → woodland/forest.
Calling savanna "desert" erases its productivity, biodiversity, and human history (cradle of hominins, pastoralism, early agriculture). It's a grassland that thinks it's a forest—or a forest that burns to stay grass.