A major controversy for understanding volcanic margin formation is whether a thermal anomaly in the mantle is required to generate the characteristic thick igneous crust. We use a fluid-dynamical model of mantle flow that includes feedback from melting on the physical properties of the mantle to study the temporal evolution of volcanic margins during continental breakup. We test how weak the mantle must be to induce small-scale convection and thus enhance melt production during breakup. We find that the mantle reference viscosity required to generate a breakup instability is sufficiently low that an unrealistic time dependence develops in the subsequent oceanic spreading system. The viscosity increase associated with dehydration melting can stabilize the system, but only at the expense of eliminating the breakup instability. An exhaustible reservoir of hot mantle resolves this inconsistency. Melt productivity increases through a deepening of the mantle solidus, while a concurrent increase in buoyancy and a decrease in viscosity in the melting region promote an initial transient phase of small-scale convection.