Bacterial growth is crucially dependent on protein synthesis and thus on the cellular abundance of ribosomes and related proteins. Here, we show that the slow diffusion of the bulky tRNA complexes in the crowded cytoplasm imposes a physical limit on the speed of translation, which ultimately limits the rate of cell growth. To study the required allocation of ancillary translational proteins to alleviate the effect of molecular crowding, we develop a model for cell growth based on a coarse-grained partitioning of the proteome. We find that coregulation of ribosome- and tRNA-affiliated proteins is consistent with measured growth-rate dependencies and results in near-optimal allocation over a broad range of growth rates. The analysis further resolves a long-standing controversy in bacterial growth physiology concerning the growth-rate dependence of translation speed and serves as a caution against premature identification of phenomenological parameters with mechanistic processes.