We examine closely the differences between the densities of vibrational states of bulk, slab, and cavity polariton modes under weak and moderate inhomogeneous broadening. While existing theoretical treatments are often based on a comparative analysis of "bare" vibrations and cavity polaritons, in the strong-coupling regime, only differences between slab/bulk polaritons on the one hand and cavity polaritons on the other hand are meaningful since "bare" vibrations are not observed experimentally. We find that polaritons in cavities significantly detuned from resonance with molecular transitions at zero in-plane wavevector do not differ appreciably from bulk polaritons in their density of vibrational states. Only cavity polaritons with sufficiently weak inhomogeneous broadening and tuned to resonance near normal incidence display a pronounced density-of-state enhancement. These results shed light on the heretofore puzzling observations of modified chemical reactivity only at zero detuning and supply a new baseline for assessing the explanatory power of proposed theories of cavity-modified chemistry.