The computational hydrogen evolution activity of Pt(111) remains controversial due to apparent discrepancies with experiments concerning rate-determining activation free energies and equilibrium hydrogen coverages. A fundamental source of error may lie within the static representations of the metal-water interface commonly employed in density functional theory (DFT)-based kinetic models neglecting important entropic effects on reaction dynamics. In this work, we present a dynamic reassessment of the Volmer-Tafel hydrogen evolution pathway on Pt(111) through DFT-based constrained molecular dynamics simulations and thermodynamic integration. Hydrogen coverage effects are gauged at two distinct surface saturations, while the critical potential dependence and constant potential conditions are accounted for using a capacitive model of the electrified interface. The uncertainty in the highly nontrivial treatment of the electrode potential is carefully examined, and we provide a quantitative estimation of the error associated with dynamically simulated electrochemical barriers. The dynamic description of the electrochemical interface promotes a substantial decrease of the Tafel free energy barrier as the coverage is increased to a full monolayer. This follows from a decreased entropic barrier due to suppressed adlayer dynamics compared to the unsaturated surface, a detail easily missed by static calculations predicting notably higher barriers at the same coverage. Due to observed endergonic adsorption of active hydrogen intermediates, the Tafel step remains rate-determining irrespective of the coverage as illustrated by composed Volmer-Tafel free energy landscapes. Importantly, our explicitly dynamic approach avoids the ambiguous choice of frozen solvent configuration, decreasing the reliance on error cancellation and paving the way for less biased electrochemical simulations.