In conventional planar growth of bulk III-V materials, a slow growth rate favors high crystallographic quality, optical quality, and purity of the resulting material. Surprisingly, we observe exactly the opposite effect for Au-assisted GaAs nanowire growth. By employing a rapid growth rate, the resulting nanowires are markedly less tapered, are free of planar crystallographic defects, and have very high purity with minimal intrinsic dopant incorporation. Importantly, carrier lifetimes are not adversely affected. These results reveal intriguing behavior in the growth of nanoscale materials, and represent a significant advance toward the rational growth of nanowires for device applications.