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.