Human sensorimotor control is remarkably fast and accurate at the system level despite severe speed-accuracy trade-offs (SATs) at the component level. The discrepancy between the contrasting SATs at these two levels is a paradox. Here we describe reaching experiments in which sensorimotor delays and quantization errors were manipulated to test their effects on reaching speed and accuracy as a surrogate for manipulating the biophysical properties. A mechanistic model was developed for how component SATs constrain sensorimotor control that is consistent with the experimental results and with Fitts' Law for reaching. The model and experiments suggest that diversity among components deconstrains their individual limitations in sensorimotor control. Such "diversity-enabled sweet spots" (DESSs) are ubiquitous in both engineering and biology, explaining why large heterogeneities exist in the components of artificial and biological systems and how both engineers and natural selection routinely evolve into systems with fast and accurate responses using imperfect components.