Wide-bandgap semiconductors such as GaN/AlGaN and ZnO/MgZnO quantum wells are promising for improving the spectral reach and high-temperature performance of terahertz quantum cascade lasers, due to their characteristically large optical phonon energies. Here, a particle-based Monte Carlo model is developed and used to quantify the potential of terahertz sources based on these materials relative to existing devices based on GaAs/AlGaAs quantum wells. Specifically, three otherwise identical quantum cascade structures based on GaN/AlGaN, ZnO/MgZnO, and GaAs/AlGaAs quantum wells are designed, and their steady-state carrier distributions are then computed as a function of temperature. The simulation results show that the larger the optical phonon energies (as in going from the AlGaAs to the MgZnO to the AlGaN materials system), the weaker the temperature dependence of the population inversion. In particular, as the temperature is increased from 10 to 300 K, the population inversions are found to decrease by factors of 4.48, 1.50, and 1.25 for the AlGaAs, MgZnO, and AlGaN structure, respectively. Based on these results, the AlGaN and MgZnO devices are then predicted to be in principle capable of laser action without cryogenic cooling.