We present a simulation study on the cosmic-ray detection capabilities of the Square Kilometre Array, the low-frequency part of which is being built in Australia. With nearly 60,000 antennas in a 1 km diameter, its antenna density is two orders of magnitude higher than at LOFAR. The wider frequency band of 50 to 350 MHz allows to resolve the radio energy footprint into smaller detail, as well as providing more information via the signal frequency spectra. We discuss the improved resolution in depth of shower maximum Xmax compared to LOFAR. Moreover, the next-level features open the possibility of measuring the longitudinal air shower profile in more detail than just its maximum Xmax, for individual air showers. The benefits are twofold: it gives additional information on the mass composition (independent of Xmax), and the main hadronic interaction models predict observable differences in longitudinal profiles and their distributions. Thus, it would help in constraining hadronic physics at energy levels beyond laboratory experiments.