As of 2023, the low-frequency part of the Square Kilometre Array will go online in Australia. It will constitute the largest and most powerful low-frequency radio-astronomical observatory to date, and will facilitate a rich science programme in astronomy and astrophysics. With modest engineering changes, it will also be able to measure cosmic rays via the radio emission from extensive air showers. The extreme antenna density and the homogeneous coverage provided by more than 60,000 antennas within an area of one km$^2$ will push radio detection of cosmic rays in the energy range around 10$^{17}$ eV to ultimate precision, with superior capabilities in the reconstruction of arrival direction, energy, and an expected depth-of-shower-maximum resolution of 6~g/cm${^2}$.