  Recently, C. M. P\'epin \textit{et al.} [Science \textbf{357}, 382 (2017)]
reported the formation of several new iron polyhydrides FeH$_x$ at pressures in
the megabar range, and spotted FeH$_5$, which forms above 130 GPa, as a
potential high-\tc \ superconductor, because of an alleged layer of dense
metallic hydrogen. Shortly after, two studies by A.~Majumdar \textit{et al.}
[Phys. Rev. B \textbf{96}, 201107 (2017)] and A.~G.~Kvashnin \textit{et al.}
[J. Phys. Chem. C \textbf{122}, 4731 (2018)] based on {\em ab initio}
Migdal-Eliashberg theory seemed to independently confirm such a conjecture. We
conversely find, on the same theoretical-numerical basis, that neither FeH$_5$
nor its precursor, FeH$_3$, shows any conventional superconductivity and
explain why this is the case. We also show that superconductivity may be
attained by transition-metal polyhydrides in the FeH$_3$ structure type by
adding more electrons to partially fill one of the Fe--H hybrid bands (as,
e.g., in NiH$_3$). Critical temperatures, however, will remain low because the
$d$--metal bonding, and not the metallic hydrogen, dominates the behavior of
electrons and phonons involved in the superconducting pairing in these
compounds.
