  In recent experiments on thin $^4$He films absorbed to rough surfaces Luhman
and Hallock [D.R. Luhman, and R.B. Hallock, Phys. Rev. Lett. \textbf{93},
086106 (2004)] attempted to observe KT features of the superfluid--normal
transition of this strongly disordered 2D bosonic system. It came as a surprise
that while peak of dissipation was measured for a wide range of surface
roughness there were no indications of the theoretically expected universal
jump of the areal superfluid density for the strongly disordered samples. We
test the hypothesis that this unusual behavior is a manifestation of
finite-size effects by numerical study of the corresponding 2D bosonic model
with strong diagonal disorder. We demonstrate that the discontinuous features
of the underlying KT transition are severely smoothed out for finite system
sizes (or finite frequency measurements). We resolve the universal
discontinuity of the areal superfluid density by fitting our data to the KT
renormalization group equations for finite systems. In analogy to our
simulations, we suggest that in experiments on strongly disordered 2D bosonic
systems the very existence of the KT scenario can and should be revealed only
from a proper finite-size scaling of the data (for $^4$He films finite-size
scaling can be effectively controlled by the scaling of finite frequency of
measurements). We also show relevance of our conclusions for a wider class of
systems, such as superconducting granular films, Josephson junction arrays, and
ultracold atomic gases, where similar difficulties appear in experiments
designed to verify KT transition (especially in disordered cases).
