The increasing penetration of inverter-based resources (IBRs), often accompanied by the displacement of synchronous generation, is changing the frequency dynamics of power systems by reducing conventional rotational inertia while increasing the potential contribution of fast active-power support. This paper investigates the combined influence of system inertia, load-frequency damping, disturbance magnitude, and IBR-based fast frequency response (FFR) using a reduced-order frequency-response model including conventional primary frequency response (PFR). A systematic sensitivity analysis is performed across different inertia, damping, and generation-loss conditions. Consistent with established frequency-response behaviour, reduced inertia results in a larger magnitude of the initial rate of change of frequency (RoCoF), deeper and earlier frequency nadirs, and a compressed corrective-action window. The effectiveness of FFR is assessed for different activation delays, showing that activation timing becomes increasingly relevant as system inertia decreases. This relationship is further investigated through a numerical FFR gain–delay capability boundary under a severe low-inertia condition. The results demonstrate that FFR effectiveness is determined not only by the magnitude of the active-power contribution but also critically by its activation timing, and that sufficiently late responses cannot necessarily be compensated by increasing the response magnitude.