Remote and in-situ observations strongly imply 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 closed plasma release. We use three-dimensional magnetohydrodynamic (3D 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. A rotational surface motion is used to approximate photospheric supergranular driving and is applied at the boundary between the coronal hole and helmet streamer. The resulting dynamics consist primarily of prolific and efficient interchange reconnection between open and closed flux. 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 the 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 motions. Our results show that these dynamics 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.