Runaway electron (RE) beams generated during disruptions pose a major threat to future high-current tokamaks. A promising mitigation approach is the benign termination scheme, in which hydrogenic material injection into the RE beam facilitates magnetohydrodynamic (MHD) events that disperse the beam before damage can occur. Despite successful demonstrations of benign termination on several tokamaks, systematic differences between medium-sized devices (DIII-D, AUG, TCV) and JET remained. Failed terminations at JET at high pre-disruptive currents >2.5 MA have left its applicability to reactor-relevant conditions uncertain. A comprehensive database study comparing JET and DIII-D identifies the internal inductance l_i, a measure of RE current profile peaking, as the key parameter governing the terminating MHD dynamics. In high-current JET cases, strongly peaked RE current profiles lead to compression to low edge safety factors. At the same time, high RE current densities suppresses recombination of the background plasma, thereby preventing benign termination. On DIII-D, terminations are primarily triggered by internal kink and coupled tearing modes, whereas on JET they are dominated by external kink modes. The termination outcome correlates with the amplitude of the MHD perturbation rather than with the (ideal) instability growth rate, challenging the previous ideal-MHD explanation of benign termination. Linear MHD modeling reproduces the experimentally observed stability boundaries and highlights the central role of resistivity in the onset of termination. Using the extended-MHD code JOREK and kinetic modeling, we identify the precise stochasticization mechanism responsible for the observed terminations and study how density and resistivity determine its outcome. In summary, this work establishes an MHD-based framework for understanding benign termination accessibility in present-day devices and identifies pathways to enable it in future reactor scenarios.