It is pointed out by Savona et al. that in the collective strong coupling regime, the motional narrowing occurs mainly for the lower polariton. The upper polariton, on the other hand, is affected by multiple scatterings which cause additional broadening. Our results are in good agreement with the experimentally observed trends . On the other hand, the linewidth expression in Eq. 21 does not change with N , so that the silver dashed line remains unchanged by varying N , which means no motional narrowing. Eqs. 34-35, on the other hand, do change with N due to the polaron decoupling effect explicitly considered in these expressions. We also have results under a smaller cavity loss rate (Γ c = 8.83 meV), see Sec. III of the Supplementary Material.