This work presents an empirical study on the design and training of iterative neural networks for image reconstruction from tomographic measurements with unknown geometry. It is based on insights gained during our participation in the recent AAPM DL-Sparse-View CT challenge and a further analysis of our winning submission (team name: robust-and-stable) subsequent to the competition period. The goal of the challenge was to identify the state of the art in sparse-view CT with data-driven techniques, thereby addressing a fundamental research question: Can neural-network-based solvers produce near-perfect reconstructions for noise-free data? We answer this in the affirmative by demonstrating that an iterative end-to-end scheme enables the computation of near-perfect solutions on the test set. Remarkably, the fanbeam geometry of the used forward model is completely inferred through a data-driven geometric calibration step.