We investigate the relationship between river channel steepness, catchment-averaged erosion rates from cosmogenic nuclides, and their potential sensitivity to cyclic precipitation rate. Using a one-dimensional longitudinal river-profile model based on the stream power law, we simulate the temporal evolution of channel steepness and erosion rates under a range of cyclic precipitation regimes. Our analysis explores the roles of sinusoidal precipitation characterized by an amplitude (<em>P_a</em>), mean (<em>P_m</em>), period, and uplift rate. We find that the ratio of precipitation amplitude to mean (<em>P_a</em> / <em>P_m</em>) is the primary control on variations in instantaneous catchment-integrated erosion rates (<em>E_in</em>), erosion rate averaged over cosmogenic nuclide accumulation time (<em>E_cos</em>), and precipitation-modified channel steepness (<em>k_s-Q</em>). These oscillations lead to deviations of <em>E_cos</em> and <em>k_s-Q</em> from uplift rates and the corresponding channel steepness, and in regions with high <em>P_a</em> / <em>P_m</em> values, the regression between erosion rate and channel steepness becomes unreliable, with extreme phase differences potentially reversing their expected relationship. To address these limitations, we introduce a new erosion rate metric, Cosmogenic-constrained cycle-mean erosion rate (<em>E_cos-Qm</em>), which represents the mean erosion rate over a climatic cycle, derived from cosmogenic nuclide concentrations combined with information on climate cyclicity. Using 1D river profile modelling, combined with <em>k_s-Qeff</em>, which is the channel steepness modified by effective precipitation over climatic cycles, we demonstrate that the relationship between <em>E_cos-Qm</em> and <em>k_s-Q</em><em>_eff</em> remains stable across sinusoidal, insolation-based and proxy-based precipitation cycles, making them more reliable indicators of long-term erosion or uplift rates. We apply this approach to granite catchments in the Three Rivers region as a natural case study to evaluate the performance of paleo-precipitation-integrated erosion rate and channel steepness metrics,<em> E_cos-Qm</em> and <em>k_s-Qeff</em>. The results demonstrate that catchments with higher <em>P_a</em> / <em>P_m</em> values exhibit larger discrepancies between <em>E_cos</em> from <em>E_cos-Qm</em>, and <em>k_sn-Q</em> from <em>k_sn-Qeff</em>, highlighting the importance of accounting for temporal precipitation variability in interpreting erosion-steepness relationships.