The fact that the flow of a hypersurface by its mean curvature can be seen as a gradient flow of the surface area has motivated an influential minimizing movement scheme (Almgren-Taylor-Wang, Luckhaus-Sturzenhecker). Also Osher's computationally efficient and very popular thresholding scheme for mean curvature flow by Osher et. al. can be interpreted as a minimizing movement scheme (Esedoglu-O.).Based on this observation, we use de Giorgi's ideas for minimizing movements in metric spaces (metric slope, variational interpolation) to give a surprisingly soft -- but conditional -- convergence proof for the thresholding scheme (Laux-0.)