  Various thin-film I$_2$-II-IV-VI$_4$ photovoltaic absorbers derived from
kesterite Cu$_2$ZnSn(S,Se)$_4$ have been synthesized, characterized, and
theoretically investigated in the past few years. The availability of this
homogeneous materials dataset is an opportunity to examine trends in their
defect properties and identify criteria to find new defect-tolerant materials
in this vast chemical space. We find that substitutions on the Zn site lead to
a smooth decrease in band tailing as the ionic radius of the substituting
cation increases. Unfortunately, this substitution strategy does not ensure the
suppression of deeper defects and non-radiative recombination. Trends across
the full dataset suggest that Gaussian and Urbach band tails in
kesterite-inspired semiconductors are two separate phenomena caused by two
different antisite defect types. Deep Urbach tails are correlated with the
calculated band gap narrowing caused by the (2I$_\mathrm{II}$+IV$_\mathrm{II}$)
defect cluster. Shallow Gaussian tails are correlated with the energy
difference between the kesterite and stannite polymorphs, which points to the
role of (I$_\mathrm{II}$+II$_\mathrm{I}$) defect clusters involving Group IB
and Group IIB atoms swapping across \textit{different} cation planes. This
finding can explain why \textit{in-plane} cation disorder and band tailing are
uncorrelated in kesterites. Our results provide quantitative criteria for
discovering new kesterite-inspired photovoltaic materials with low band
tailing.
