Reductions of the ionospheric cross polar cap potential in magnetohydrodynamic models that include polar wind-like heavy ion outflow have become a ubiquitous observation in recent studies. The underlying mechanisms for these reductions, which are not to be confused with the problem of potential saturation, remain in question. A possible explanation is that such outflow inflates the magnetosphere, creating a blunter obstacle to the solar wind and reducing the upstream geoeffective length. Such an explanation is attractive because it describes the outflow-related potential drop in clear, model-independent terms. This study uses three separate magnetohydrodynamic simulations to test this hypothesis: one coupled to a polar wind outflow model, one coupled to an inner magnetosphere code in order to reproduce the effect without explicit outflow, and a stand-alone baseline simulation. It is found that this hypothesis cannot explain the total reduction. Results suggest that other mechanisms, such as a change to the dayside reconnection rate, may be important, but further investigation is required.