By means of the Discrete Element Method, we investigate the relationship between the power‐law exponent of the grain size distribution (GSD) and the mobility of granular transitional flows. This is done with the aim of testing a recently posed hypothesis, suggesting that high power‐law exponents are related to the large mobility observed in natural mass flows (Lai et al., 2017, https://doi.org/10.1002/2017gl075689), as a consequence of a lubrication mechanism in which small grains act as rotational bearings reducing the shear strength of the flowing mass. We show that both the mobility of the flow and the shear strength of the material are independent of the GSD power‐law exponent, as long as the system‐to‐grain size ratio of the studied system is sufficiently large, as it is expected in natural granular flows. This confirms that the power‐law exponent, or the proportion of small and big grains, are not plausible origins of the large mobility of granular avalanches.