  We elaborate on the recently introduced concept of reentrant Kondo effect in
quantum impurities/dots coupled to hybrid metal-semiconductor contacts
[G.~Diniz {\em et al.}, Phys. Rev. B {\bf 101}, 125115 (2020)]. By noticing the
equivalence of the originally suggested semiconducting arrangement to an
analogous three-terminal quantum dot setup with a normal and two phase-biased
superconducting leads introduced in our recent work [Phys. Rev. B {\bf 103},
035419 (2021)], we put this effect into a new physical context, which enables
us a fresh look on the problem. First, we identify the superconducting
counterpart of the reentrant Kondo effect and, consequently, reveal its
fragility with respect to an underlying doublet-singlet quantum phase
transition induced by the particle-hole asymmetry of the reservoir densities of
states. This is pertinent (even if previously unnoticed) also in the original
as well as extended semiconducting setups, where it puts stringent conditions
on the symmetry of the contact density of states. Furthermore, we analyze
experimental feasibility of observing the reentrant Kondo effect in its
superconducting realization concluding that even present day experiments might
see the onset of the reentrant behavior, but fully developed Kondo features
cannot be reached due to the required vast separation of energy/temperature
scales.
