Why are there few trees in the steppes, savannas and deserts?

Most trees need constant moisture to grow, but a lot of moisture is needed for trees to form a forest or grove. And in such ecosystems as steppe, desert or savannah there is little moisture, precipitation is unstable, groundwater is very deep. All this makes it impossible for trees to reproduce. But in the steppes and savannas, due to the lack of trees and access to the sun, grasses and shrubs have proliferated. And most deserts are unsuitable for even grass growth, since there is almost no rainfall.