An excess of gamma rays has been identified at the centre of the Milky Way, and annihilation of dark matter has been posited as a potential source. This hypothesis faces significant challenges: difficulty characterizing astrophysical backgrounds, the need for a non-trivial adiabatic contraction of the inner part of the Milky Way's dark matter halo, and recent observations of photon clustering, which suggest that the majority of the excess is due to unresolved point sources. Here we point out that the apparent point-like nature of the emission rules out the dark matter interpretation of the excess entirely. Attempting to model the emission with dark matter point sources either worsens the problem with the inner slope, requires an unrealistically large minihalo fraction toward the Galactic Centre, or overproduces the observed emission at higher latitudes.