While deep neural networks have shown impressive results in automatic speaker recognition and related tasks, it is dissatisfactory how little is understood about what exactly is responsible for these results. Part of the success has been attributed in prior work to their capability to model supra-segmental temporal information (SST), i.e., learn rhythmic-prosodic characteristics of speech in addition to spectral features. In this paper, we (i) present and apply a novel test to quantify to what extent the performance of state-of-the-art neural networks for speaker recognition can be explained by modeling SST; and (ii) present several means to force respective nets to focus more on SST and evaluate their merits. We find that a variety of CNN- and RNN-based neural network architectures for speaker recognition do not model SST to any sufficient degree, even when forced. The results provide a highly relevant basis for impactful future research into better exploitation of the full speech signal and give insights into the inner workings of such networks, enhancing explainability of deep learning for speech technologies.