  We demonstrate that Debye shielding cannot be employed to constrain the
cosmological abundance of magnetic monopoles, contrary to what is stated in the
previous literature. Current model-independent bounds on the monopole abundance
are then revisited for unit Dirac magnetic charge. We find that the Andromeda
Parker bound can be employed to set an upper limit on the monopole flux at the
level of $F_M\lesssim 5.3\times
10^{-19}\,\text{cm}^{-2}\text{s}^{-1}\text{sr}^{-1}$ for a monopole mass
$10^{13}\,\text{GeV}/c^2\lesssim m\lesssim 10^{16}\,\text{GeV}/c^2$, which is
more stringent than the MACRO direct search limit by two orders of magnitude.
This translates into stringent constraints on the monopole density parameter
$\Omega_M$ at the level of $10^{-7}-10^{-4}$ depending on the mass. For larger
monopole masses the scenarios in which magnetic monopoles account for all or
the majority of dark matter are disfavored.
