Recently, Climent, Subotnik, and Nitzan applied the Kubo-Anderson classical stochastic theory of molecular spectral lineshape to the case of polaritons formed in the collective strong coupling regime. By including only one cavity mode which collectively interacts with many molecules, they provided simple analytic results in the fast and slow limits of the disorder dynamics and can be evaluated numerically for the intermediate case. In particular, the polariton linewidth scales like 1/ √ N under the slow limit. Despite the theoretical success in Ref. , we want to emphasize that the Kubo-Anderson theory is classical and Markovian. It predicts that no narrowing effect can be exhibited under the fast limit , and does not explain the experimentally observed asymmetry between the UP and LP linewidths. Moreover, Ref. 31 focused on the resonant case and lacked the discussion for general detuned cases. With regard to these limitations, new theoretical and numerical efforts are urgently needed, in which a fully quantum mechanical description of the phonon environment should be emphasized.