jats:titleAbstract</jats:title> jats:pWe investigate the luminosity suppression and its effect on the mass–radius relation and cooling evolution of highly magnetized white dwarfs. Based on the effect of magnetic field relative to gravitational energy, we suitably modify our treatment of the radiative opacity, magnetostatic equilibrium, and degenerate core equation of state to obtain the structural properties of these stars. Although the Chandrasekhar mass limit is retained in the absence of magnetic field and irrespective of the luminosity, strong central fields of about 10jats:sup14</jats:sup> G can yield super-Chandrasekhar white dwarfs with masses ∼2.0 jats:italicM</jats:italic> jats:sub⊙</jats:sub>. Smaller white dwarfs tend to remain super-Chandrasekhar for sufficiently strong central fields even when their luminosity is significantly suppressed to 10jats:sup−16</jats:sup> jats:italicL</jats:italic> jats:sub⊙</jats:sub>. Nevertheless, owing to the cooling evolution and simultaneous field decay over 10 Gyr, the limiting masses of small magnetized white dwarfs can fall to 1.5 jats:italicM</jats:italic> jats:sub⊙</jats:sub> over time. However, the majority of these systems still remain practically hidden throughout their cooling evolution because of their high fields and correspondingly low luminosities. Utilizing the stellar evolution code jats:scstars</jats:sc>, we obtain close agreement with the analytical mass limit estimates, which suggests that our analytical formalism is physically motivated. Our results argue that super-Chandrasekhar white dwarfs born as a result of strong-field effects may not remain so forever. This explains their apparent scarcity, in addition to making them hard to detect because of their suppressed luminosities.</jats:p>