Very interesting point! (Though for non-homogeneous but still isotropic universes there still exist spherical harmonics, so homogeneity doesn't seem like a crit

Very interesting point! (Though for non-homogeneous but still isotropic universes there still exist spherical harmonics, so homogeneity doesn't seem like a critical restriction here. Those are used, for instance, to analyze non-homogeneous alternatives to the usual FLRW cosmological model, e.g. Lemaître-Tolman-Bondi (LTB) models.)