The calibration-free Budyko model is capable of predicting streamflow with reasonable accuracy using only meteorological information at timescales greater than one year. However, hydrological models suitable for small timescales typically require extensive streamflow data for calibration. Taking a cue from the Budyko model, a Dynamic Budyko (DB) model was proposed to simulate runoff-generation at small timescales with a universally constant power-law parameter obtained through recession flow analysis (referred to as DBv1 here). In this study, we propose an improved DB model (DBv2) that uses a universally constant exponential parameter reported in earlier literature. Considering daily data from 975 US basins, we show that DBv2 is significantly better than DBv1 for runoff generation simulation when both models use the same routing function. We then compared DBv2 with two established hydrological models, HBV and GR4J, allowing all three models to use the same routing module having two parallel linear reservoirs (DBv2LR, HBVLR and GR4JLR; the subscript LR refers to the linear routing structure). The DBv2LR, which is calibrated only for runoff-routing, performs as good as fully calibrated HBVLR and GR4JLR, with median NSE values being close to 0.65 for all three models. The results here contradict the earlier notion that runoff-generation modelling is more complicated than runoff-routing. Our study, thus, is the latest to suggest that a paradigm shift is needed for advancing rainfall-runoff modelling further by focusing on developing climate-centric hydrological models requiring no calibration rather than developing soil-centric models with multiple free-parameters.