Hot-carrier cooling (HCC) in metal halide perovskites in the high-density regime is significantly slower compared to conventional semiconductors. This effect is commonly attributed to a hot-phonon bottleneck but the influence of the lattice properties on the HCC behaviour is poorly understood. Using pressure-dependent transient absorption spectroscopy (fs-TAS) we find that at an excitation density below Mott transition, pressure does not affect the HCC. On the contrary, above Mott transition, HCC in methylammonium lead iodide (MAPbI3) is around two times as fast at 0.3 GPa compared to ambient pressure. Our electron-phonon coupling calculations reveal about two times stronger electron-phonon coupling for the inorganic cage mode at 0.3 GPa. However, our experiments reveal that pressure promotes faster HCC only above Mott transition. Altogether, these findings suggest a change in the nature of excited carriers in the high-density regime, providing insights on the electronic behavior of devices operating at such high charge-carrier density.