Species richness varies immensely around the world. Variation in the rate of diversification (speciation minus extinction) is often hypothesized to explain this pattern, while alternative explanations invoke time or ecological carrying capacities as drivers. Focusing on seed plants, the world’s most important engineers of terrestrial ecosystems, we investigated the role of diversification rate as a link between the environment and global species richness patterns. Applying structural equation modeling to a comprehensive distribution dataset and phylogenetic tree covering all circa 332,000 seed plant species and 99.9% of the world’s terrestrial surface (excluding Antarctica), we test five broad hypotheses postulating that diversification serves as a mechanistic link between species richness and climate, climatic stability, seasonality, environmental heterogeneity, or the distribution of biomes. Our results show that the global patterns of species richness and diversification rate are entirely independent. Diversification rates were not highest in warm and wet climates, running counter to the Metabolic Theory of Ecology, one of the dominant explanations for global gradients in species richness. Instead, diversification rates were highest in edaphically diverse, dry areas that have experienced climate change during the Neogene. Meanwhile, we confirmed climate and environmental heterogeneity as the main drivers of species richness, but these effects did not involve diversification rates as a mechanistic link, calling for alternative explanations. We conclude that high species richness is likely driven by the antiquity of wet tropical areas (supporting the “tropical conservatism hypothesis”) or the high ecological carrying capacity of warm, wet, and/or environmentally heterogeneous environments.