We investigate numerically and analytically the effects of hydrodynamics on the dynamics of topological defects in p-atic liquid crystals, i.e., two-dimensional liquid crystals with p-fold rotational symmetry. Importantly, we find that hydrodynamics fuels a generic passive self-propulsion mechanism for defects of winding number s ¼ ðp − 1Þ=p and arbitrary p. Strikingly, we discover that hydrodynamics always accelerates the annihilation dynamics of pairs of AE1=p defects and that, contrary to expectations, this effect increases with p. Our Letter paves the way toward understanding cell intercalation and other remodeling events in epithelial layers.