Despite their great performance over the years, handcrafted speech features are not necessarily optimal for any particular speech application. Consequently, with greater or lesser success, optimal filterbank learning has been studied for different speech processing tasks. In this paper, we fill in a gap by exploring filterbank learning for keyword spotting (KWS). Two approaches are examined: filterbank matrix learning in the power spectral domain and parameter learning of a psychoacoustically-motivated gammachirp filterbank. Filterbank parameters are optimized jointly with a modern deep residual neural network-based KWS back-end. Our experimental results reveal that, in general, there are no statistically significant differences, in terms of KWS accuracy, between using a learned filterbank and handcrafted speech features. Thus, while we conclude that the latter are still a wise choice when using modern KWS back-ends, we also hypothesize that this could be a symptom of information redundancy, which opens up new research possibilities in the field of small-footprint KWS.