Genetic drift at the frontiers of two-dimensional range expansions of microorganisms can frustrate local cooperation between different genetic variants, demixing the population into distinct sectors. In a biological context, mutualistic or antagonistic interactions will typically be asymmetric between variants. By taking into account both the asymmetry and the interaction strength, we show that the much weaker demixing in three dimensions allows for a mutualistic phase over a much wider range of asymmetric cooperative benefits, with mutualism prevailing for any positive, symmetric benefit. We also demonstrate that expansions with undulating fronts roughen dramatically at the boundaries of the mutualistic phase, with severe consequences for the population genetics along the transition lines.