With the aim of characterizing the role played by magnetic fields in the formation of young protostars, several recent studies have revealed unprecedented features toward high angular resolution ALMA dust polarization observations of Class 0 protostellar cores. Observations of polarized dust emission allow us to investigate the physical processes involved in the Radiative Alignment Torques (RATs) acting on dust grains from the core to disk scales, that align the angular momentum of grains with magnetic field. We find that the dust polarization is enhanced along the cavity walls of bipolar outflows, which are subject to high irradiation from the reprocessed radiation field emanating from the center of the protostar. In addition, highly polarized dust thermal emission has been detected in region most likely linked with the infalling envelope, in the form of filamentary structure being potential magnetized accretion streamer. Notably, we propose that the polarized emission we see at millimeter wavelengths along the irradiated cavity walls can be reconciled with the expectations of RAT theory if the aligned grains present in these cavities have grown larger than what is typically expected in young protostellar cores. To approach an estimation of the efficiency of dust alignment in protostars, we gathered a large sample of ALMA dust polarization observations of Class 0 protostars in order to perform a statistical analysis examining the trend between the dispersion of polarization position angles and the fractional polarization. We report a significant correlation between these two quantities, whose power-law index differs significantly from the one observed by Planck in star-forming clouds, confirming the different nature for the disorganized component of magnetic fields at the scales of protostellar envelopes. The grain alignment efficiency, is surprisingly constant across three orders of magnitude in envelope column density. Synthetic observations of non-ideal magneto-hydrodynamic simulations of protostellar cores implementing RATs, show that the ALMA values of grain alignment efficiency lie among those predicted by a perfect alignment of grains, and are significantly higher than the ones obtained with RATs. Ultimately, our results suggest dust alignment mechanism(s) are efficient at producing polarized dust emission in the local conditions typical of Class 0 protostars. The grain alignment efficiency found in these objects seems to be higher than the efficiency produced by the standard RAT alignment of paramagnetic grains. We performed further detailed modelling of the protostellar inner envelope physical conditions, alongside tentative comparisons between ALMA molecular line observations of UV-sensitive chemical tracers and dust polarization observations. We found that indeed, grains with super-paramagnetic inclusions, significant irradiation conditions (qualitatively comforted by the chemical observations), and large grains (10 μm) of compact structure are necessary to reproduce the observed grain alignment efficiency. However, further studies leading to a better characterization of dust grain characteristics, and additional grain alignment mechanisms, will be required to investigate deeper the cause of strong polarized dust emission located in regions of the envelope where alignment conditions are not favorable.