Accurate inclusion of both spin precession and orbital eccentricity effects in gravitational waveform models represents a key hurdle in our ability to fully characterize the properties of compact binaries. Virtually all efforts to model precession rely on a coprecessing frame transformation, a time-dependent spatial rotation that tracks the dominant emission direction and simplifies the waveform morphology. We assess the utility of the coprecessing frame transformation to separate out the effect of the precession of the orbital plane from the waveform in the presence of non-negligible orbital eccentricity. We rely on $20$ numerical relativity simulations, which include the complete physical effects of spin precession and eccentricity in the strong-field, and compare waveforms in both the inertial and coprecessing frames. Comparing against the eccentric, spin-aligned model SEOBNRv5EHM, we find that while the waveform mismatches decrease in the coprecessing frame, they remain above the level required for accurate waveform modeling, $\sim 0.01$ or higher for large inclinations. Further improvements, e.g., modeling mode asymmetries as already pursued for quasicircular binaries, will likely prove essential. We also find that by removing the dominant amplitude and phase modulations from the waveform, the coprecessing frame facilitates surrogate modeling, achieving lower errors at a fixed number of basis elements compared to the inertial frame. Our results demonstrate both the utility and the limitations of the coprecessing frame as a cornerstone in waveform modeling for eccentric and precessing binaries.