Despite its unphysical tip singularity and the violation of the angular momentum balance, the classical uniformly-loaded propeller without wake rotation still represents the benchmark model both for theoretical and practical applications. The model originates from the so-called Axial Momentum Theory which is further simplified removing the radial variability of the load. However, as well-known, some mathematical simplifications are customarily introduced in this theory when the axial momentum equation is applied in a differential form. Yet, the available literature generally seems to disregard their impact on the accuracy of the predicted flow. In this paper, the errors introduced by these simplifying assumptions are evaluated by comparing the results of the aforementioned theory with those of an actuator disk approach which models the propeller wake through a force-free ring-vortex sheet. The comparison shows that significant local errors arise in the tip region, especially for highly loaded rotors.