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Remote and in-situ observations suggest that the slow solar wind consists of plasma from the hot, closed-field corona that is released onto open magnetic field lines. The Separatrix-Web (S-Web) theory for the slow wind proposes that photospheric motions, at the scale of supergranules, are responsible for generating dynamics at coronal-hole boundaries, which result in the inferred necessary transfer of plasma from closed to open field lines. We use 3D magnetohydrodynamic (MHD) simulations to determine the effect of photospheric flows on the open and closed magnetic flux of a model corona with a dipole magnetic field and an isothermal solar wind. We find that a supergranular-scale photospheric motion at the boundary between the coronal hole and helmet streamer results in prolific and efficient interchange reconnection between open and closed flux. This reconnection acts to smooth the large- and small-scale structure introduced by the photospheric flows. Magnetic flux near the coronal-hole boundary experiences multiple interchange events, with some flux interchanging over fifty times in one day. Additionally, we find that this interchange reconnection occurs all along the coronal-hole boundary, even producing a lasting change in magnetic-field connectivity in regions that were not driven by the applied photospheric motions. Our results imply that interchange reconnection is the dominant form of dynamics along open-closed boundaries and should be ubiquitous in the Sun and heliosphere. We discuss the implications of our simulations for understanding the observed properties of the slow solar wind, with particular focus on the global-scale consequences of interchange reconnection.