We present a reassessment of the radial abundance gradients of He, C, N, O, Ne, S, Cl, and Ar in the Milky Way using the deep optical spectra of 42 HII regions presented in Arellano-Córdova et al. (2020, 2021) and Méndez-Delgado et al. (2020) exploring the impact of: (1) new distance determinations based on Gaia EDR3 parallaxes and (2) the use of Peimbert's temperature fluctuations paradigm ($t ^ 2> 0$) for deriving ionic abundances. We find that distances based on Gaia EDR3 data are more consistent with kinematic ones based on Galactic rotation curves calibrated with radio parallaxes, which give less dispersion and uncertainties than those calibrated with spectrophotometric stellar distances. The distances based on the Gaia parallaxes --DR2 or EDR3-- eliminate the internal flattening observed in previous determinations of the Galactic gradients at smaller distances than $\sim 7$ kpc. Abundances and gradients determined assuming $ t ^ 2> 0 $ -- not only for O but also for the rest of elements -- are not affected by the abundance discrepancy problem and give elemental abundances much consistent with the solar ones for most elements. We find that our radial abundance gradient of He is consistent with the most accurate estimates of the primordial He abundance. We do not find evidence of azimuthal variations in the chemical abundances of our sample. Moreover, the small dispersion in the O gradient -- indicator of metallicity in photoionized regions -- indicate that the gas of the HII regions is well mixed in the sampled areas of the Galaxy.