  Garc\'ia-Aguilar et al. [Phys. Rev. Lett 126, 038001 (2021)] have shown that
the deformations of "shape-shifting droplets" are consistent with an elastic
model, that, unlike previous models, includes the intrinsic curvature of the
frozen surfactant layer. In this Comment, we show that the interplay between
surface tension and intrinsic curvature in their model is in fact
mathematically equivalent to a physically very different phase-transition
mechanism of the same process that we developed previously [Phys. Rev. Lett.
118, 088001 (2017); Phys. Rev. Res. 1, 023017 (2019)]. The mathematical models
cannot therefore distinguish between the two mechanisms, and hence it is not
possible to claim that one mechanism underlies all observed shape-shifting
phenomena without a much more detailed comparison of experiment and theory.
