We investigate the scope of the organocatalyzed step-growth copolymerization of CO2-sourced exovinylene bicyclic carbonates with bio-based diols into polycarbonates. A series of regioregular poly(oxo-carbonate)s were prepared from sugar- (1,4-butanediol and isosorbide) or lignin-derived (1,4-benzenedimethanol and 1,4-cyclohexanediol) diols at 25 °C with 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU) as a catalyst, and their defect-free structure was confirmed by nuclear magnetic resonance spectroscopy studies. Their characterization by differential scanning calorimetry and wide-angle X-ray scattering showed that most of them were able to crystallize. When the polymerizations were carried out at 80 °C, some structural defects were introduced within the polycarbonate chains, which limited the polymer molar mass. Model reactions were carried out to understand the influence of the structure of alcohols, the temperature (25 or 80 °C), and the use of DBU on the rate of alcoholysis of the carbonate and on the product/linkage selectivity. A full mechanistic understanding was given by means of static- and dynamic-based density functional theory (DFT) calculations showing the determining role of DBU in the stability of intermediates, and its important role in the rate-determining steps is revealed. Furthermore, the origin of side reactions observed at 80 °C was discussed and rationalized by DFT modeling. As impressive diversified bio-based diols are accessible on a large scale and at low cost, this process of valorization of carbon dioxide gives new perspectives on the sustainable production of bioplastics under mild conditions.