<p>The physical and mathematical properties of charged black holes that are linearly coupled to charged massive scalar fields are studied analytically. In particular, we prove that, in the eikonal large-mass regime <i>Mμ</i> ≫ 1, the compact dimensionless inequality Φ_H &gt; <i>Q</i>/<i>M</i> provides a sufficient condition for the development of superradiant instabilities in the curved black-hole spacetime [here {<i>M</i>, <i>Q</i>, Φ_H} are respectively the mass, the electric charge, and the horizon electrostatic potential of the central black hole and <i>μ</i> is the proper mass of the field]. The familiar charged Reissner-Nordström black hole does not satisfy this inequality. On the other hand, we explicitly prove that all charged Ayón-Beato-García (ABG) black-hole spacetimes satisfy this analytically derived sufficient condition and may therefore become superradiantly unstable to perturbations of charged massive scalar fields.</p>