  In 2023, Cristoferi, Fonseca and Ganedi proved that Cahn-Hilliard type
energies with spatially inhomogeneous potentials converge to the usual
(isotropic and homogeneous) perimeter functional if the length-scale $\delta$
of spatial inhomogeneity in the double-well potential is small compared to the
length-scale $\varepsilon$ of phase transitions. We give a simple new proof
under a slightly stronger assumption on the regularity of $W$ with respect to
the phase parameter. The simplicity of the proof allows us to easily find
multiple generalizations in other directions, including stochastic potentials
and potentials which may become zero outside the wells ('voids'). The
theoretical results are complemented by numerical experiments.
  Our main message is that, across a wide variety of settings, nothing that
looks sufficiently homogeneous at the transition length scale between phases,
affects the limiting behavior in the slightest. The notable exception is the
setting of potentials with spatially varying potential wells, where a stronger
scale separation $\delta \ll \varepsilon^{3/2}$ is needed. Based on the
analysis, we further provide a modified Modica-Mortola type energy which does
not require such a scale separation.
  The theoretical analysis is complemented by numerical experiments.
