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 $X_{\rm max}$ 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 $X_{\rm max}$ , for individual air showers. The benefits are twofold: it gives additional
information on the mass composition (independent of $X_{\rm max}$), 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.