Models in which scalar field dark energy interacts with dark matter via a pure momentum coupling have previously been found to potentially ease the structure formation tension between early-and late-universe observations. In this article we explore the physical mechanism underlying this feature. We argue analytically that the perturbation growth equations imply the suppression of structure growth, illustrating our discussion with numerical calculations. Then we generalise the previously studied quadratic coupling between the dark energy and dark matter to a more general power law case, also allowing for the slope of the dark energy exponential potential to vary. We find that the structure growth suppression is a generic feature of power law...