Why aren't there very many trees in the grasslands biome?
There isn't much water.
Grasslands actually get fairly little rainfall, so it's very difficult for trees to be permanent settlers in grasslands biomes. However, since grass is seasonal and can grow and reproduce very quickly, it really only needs one streak of rain to sprout, grow, and reproduce.
Trees need consistent water, and they need it for long periods of time to grow, and often they need years before they even produce seeds. Since for them, most of the year in a grassland is a barren desert, their seeds rarely germinate, and even more rarely survive to grow at all.