  Interfacing bulk conducting topological Bi$_2$Se$_3$ films with s-wave
superconductors initiates strong superconducting order in the nontrivial
surface states. However, bulk insulating topological
(Bi$_{1-x}$Sb$_{x})_2$Te$_3$ films on bulk Nb instead exhibit a giant
attenuation of surface superconductivity, even for films only two-layers thick.
This massive suppression of proximity pairing is evidenced by
ultrahigh-resolution band mappings and by contrasting quantified
superconducting gaps with those of heavily n-doped topological Bi$_2$Se$_3$/Nb.
The results underscore the limitations of using superconducting proximity
effects to realize topological superconductivity in nearly intrinsic systems.
