In gravel-bed rivers, deterministic approaches to predicting bedload transport use the mean bed shear stress (termed one-dimensional or ‘1D’ equations) or integrate across the frequency distribution of shear stress (2D equations). At low flows, incorporating a range of shear stress values increases prediction accuracy, but at relatively high flows the 1D and 2D approaches are similarly accurate. We contribute to an understanding of the stage-dependent relationship between morphology and bedload transport, and specifically why the mean shear stress characterises transport capacity at formative discharges. We performed physical modelling using a generic Froude-scaled model of a steep laterally-constrained gravel-bed river and captured digital elevation models to perform 2D hydraulic modelling. Both 1D and 2D Meyer-Peter Müller equations were highly accurate across two distinct channel morphologies. In alternate bar channels, transport capacity was controlled by negative feedbacks between flow depth and local bed slope that resulted in a relatively homogeneous distribution of bed shear stress. In plane-bed channels, which lacked the degrees-of-freedom available for large-scale morphologic adjustment, transport capacity was controlled by a spatially variable migrating surface texture. The contrasting spatial patterns of morphology, hydraulics, and surface texture between the two channel morphologies highlight the potential for the same correlation between mean shear stress and transport capacity to emerge through different mechanisms. We suggest that nonlinear feedbacks explain why simple bedload transport equations can be highly effective above a certain flow stage across a range of channel morphologies, and further work should examine whether lateral adjustment confounds this result.