Tram et al. 2016 recently pointed out in [1] that power-law inflation in presence of a dark radiation component may relieve the 3.3 σ tension which exists within standard ΛCDM between the determination of the local value of the Hubble constant by Riess et al. (2016) [2] and the value derived from CMB anisotropy data [3] by the Planck collaboration. In this comment, we simply point out that this interesting proposal does not help in solving the σ8 tension between the Planck data and, e.g., the weak lensing measurements. Moreover, when the latest constraints on the reionization optical depth obtained from Planck HFI data [4] are included in the analysis, the H0 tension reappears and this scenario looses appeal.