Human sensorimotor control exhibits remarkable speed and accuracy, and the tradeoff between them is encapsulated in Fitts' Law for reaching and pointing. While Fitts related this to Shannon's channel capacity theorem, despite widespread study of Fitts' Law, a theory that connects implementation of sensorimotor control at the system and hardware level has not emerged. Here we describe a theory that connects hardware (neurons and muscles with inherent severe speed-accuracy tradeoffs) with system level control to explain Fitts' Law for reaching and related laws. The results supporting the theory show that diversity between hardware components is exploited to achieve both fast and accurate control performance despite slow or inaccurate hardware. Such "diversity-enabled sweet spots" (DESSs) are ubiquitous in biology and technology, and explain why large heterogeneities exist in biological and technical components and how both engineers and natural selection routinely evolve fast and accurate systems using imperfect hardware.