Upon neutron irradiation by ${10}^{18}$ neutrons/${\mathrm{cm}}^{2}$, Eg1 MeV, the superconducting transition temperatures of ${\mathrm{UBe}}_{13}$ and ${\mathrm{UPt}}_{3}$ fall by 40% and 60%, respectively---a factor of 3 more rapid than found in any other superconductor. We argue that this extreme sensitivity of heavy-fermion superconductors (HFS's) to neutron-irradiation-induced defects does not serve as evidence for unconventional pairing, since the defects produced apparently act as magnetic impurities. Such ease of magnetic impurity formation in HFS's, already found in ${\mathrm{UPt}}_{3}$ by chemical doping, makes any attempt to investigate unconventional pairing via introduction of nonmagnetic defects more difficult. The neutron irradiation severely affects the low-temperature spin-fluctuation specific heat of ${\mathrm{UPt}}_{3}$. An explanation for the drastic suppression of ${T}_{c}$ by doping with ``nonmagnetic'' Cu in ${\mathrm{UBe}}_{13}$ is proposed.