  Topological insulators and superconductors support extended surface states
protected against the otherwise localizing effects of static disorder.
Specifically, in the Wigner-Dyson insulators belonging to the symmetry classes
A, AI, and AII, a band of extended surface states is continuously connected to
a likewise extended set of bulk states forming a ``bridge'' between different
surfaces via the mechanism of spectral flow. In this work we show that this
mechanism is absent in the majority of non-Wigner-Dyson topological
superconductors and chiral topological insulators. In these systems, there is
precisely one point with granted extended states, the center of the band,
$E=0$. Away from it, states are spatially localized, or can be made so by the
addition of spatially local potentials. Considering the three-dimensional
insulator in class AIII and winding number $\nu=1$ as a paradigmatic case
study, we discuss the physical principles behind this phenomenon, and its
methodological and applied consequences. In particular, we show that low-energy
Dirac approximations in the description of surface states can be treacherous in
that they tend to conceal the localizability phenomenon. We also identify
markers defined in terms of Berry curvature as measures for the degree of state
localization in lattice models, and back our analytical predictions by
extensive numerical simulations. A main conclusion of this work is that the
surface phenomenology of non-Wigner-Dyson topological insulators is a lot
richer than that of their Wigner-Dyson siblings, extreme limits being
spectrum-wide quantum critical delocalization of all states vs. full
localization except at the $E=0$ critical point. As part of our study we
identify possible experimental signatures distinguishing between these
different alternatives in transport or tunnel spectroscopy.
