  Kondo insulators are strongly correlated system in which a clean insulating
gap emerges only at very low temperature due to many-body effects involving
localized $f$-electrons. However, certain Kondo insulators, like SmB$_6$ and
Ce${_3}$Bi${_4}$Pt${_3}$, display metallic behaviors at extremely low
temperatures, that have defied current understanding. Recent advances in
topological effects in materials has raised the attention on the protected
surface states in these "topological Kondo insulators" as a potential
resolution to some of the puzzling behaviors. Here we resolve these puzzles via
a different route, by showing that the emergent Kondo insulating scale is
extremely vulnerable against moderate degree of disorder, such that the gap is
filled with a small number of states. Therefore, the real samples are probably
never truly insulating and this in turn compromises the essential building
block of topological considerations. Our results suggest strongly that systems
like the Slater insulators would be a more promising direction to extend the
realm of topology to strongly correlated systems.
