Contemporary deep speech enhancement (SE) models are often trained with specific auxiliary terms in the loss function as a way to improve their performance in terms of perceptual metrics. Nevertheless, a higher score on a perceptual metric does not necessarily correlate with an improved listening experience. Through objective and subjective experiments, we assess the performance of SE models trained with two different types of auxiliary PESQ loss terms. The numerical evaluation on a suite of standard metrics suggests that, while models optimized for PESQ naturally obtain higher PESQ scores in the test set, for most other metrics the scores do not significantly change. In some cases, the PESQ loss even results in worse PESQ scores on mismatched data. A formal listening experiment reveals that the models without a PESQ loss were generally preferred over models that include it, across all settings. Finally, we analyze the relative importance of PESQ in the composite metrics CSIG, CBAK and COVL, and find that PESQ dominates all of them. Our study highlights the perils of over-reliance on PESQ and stresses the importance of a complete evaluation procedure for SE.