Machine-learning models, particularly the Long Short-Term Memory (LSTM) networks, have recently shown strong performance in streamflow prediction, often outperforming process-based rainfall–runoff models. However, the causes of the comparatively weaker performance of process-based models remain insufficiently understood. In the present study, we hypothesize that deficiencies in channel routing module limit the ability of process based models to capture the nonlinear dynamics of runoff propagation. To test this hypothesis, we coupled the HBV rainfall-runoff model with the recently proposed Iterative Routing Model (IRM), which dynamically updates flow velocity as a function of streamflow. Across 64 CAMELS catchments, the HBV–IRM framework improved median NSE from 0.65 (HBV) to 0.72 and approached the global LSTM benchmarks (median NSE = 0.74). The findings highlight the importance of nonlinear routing in process-based models and demonstrate that improvements in the routing module can narrow the performance gap with machine-learning approaches.