Recently, C. M. Pépin et al. [Science 357, 382 (2017)] reported the formation of several new iron polyhydrides FeHx at pressures in the megabar range and spotted FeH5, 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 et al. [Phys. Rev. B 96, 201107 (2017)] and A. G. Kvashnin et al. [J. Phys. Chem. C 122, 4731 (2018)] based on ab initio Migdal-Eliashberg theory seemed to independently confirm such a conjecture. We conversely find, on the same theoretical-numerical basis, that neither FeH5 nor its precursor, FeH3, 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 FeH3 structure type by adding more electrons to partially fill one of the Fe-H hybrid bands (as, e.g., in NiH3). 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.