The size and density of stomatal pores limit the maximum rate of leaf carbon gain and water loss ($g_\text{max}$) in land plants. The limits of $g_\text{max}$ due to anatomy, and its constraint by the negative correlation of stomatal size and density at broad phylogenetic scales, has been unclear and controversial. The prevailing hypothesis posits that adaptation to higher $g_\text{max}$ is typically constrained by geometry and/or an economic need to reduce the allocation of epidermal area to stomata (stomatal-area minimization), and this would require the evolution of greater numbers of smaller stomata. Another view, supported by the data, is that across plant diversity, epidermal area allocated to guard cells versus other cells can be optimized without major trade-offs, and higher $g_\text{max}$ would typically be achieved with a higher allocation of epidermal area to stomata (stomatal-area increase). We tested these hypotheses by comparing their predictions for the structure of the covariance of stomatal size and density across species, applying macroevolutionary models and phylogenetic regression to data for 2408 species of angiosperms, gymnosperms, and ferns from forests worldwide. The observed stomatal size-density scaling and covariance supported the stomatal-area increase hypothesis for high $g_\text{max}$. A higher $g_\text{max}$ involves construction costs and maintenance costs that should be considered in models assessing optimal stomatal conductance for predictions of water use, photosynthesis, and water-use efficiency as influences on crop productivity or in Earth System models.