Kinetic proofreading is an error correction mechanism present in the processes of the central dogma and beyond and typically requires the free energy of nucleotide hydrolysis for its operation. Though the molecular players of many biological proofreading schemes are known, our understanding of how energy consumption is managed to promote fidelity remains incomplete. In our work, we introduce an alternative conceptual scheme called "the piston model of proofreading" in which enzyme activation through hydrolysis is replaced with allosteric activation achieved through mechanical work performed by a piston on regulatory ligands. Inspired by Feynman's ratchet and pawl mechanism, we consider a mechanical engine designed to drive the piston actions powered by a lowering weight, whose function is analogous to that of ATP synthase in cells. Thanks to its mechanical design, the piston model allows us to tune the "knobs" of the driving engine and probe the graded changes and trade-offs between speed, fidelity, and energy dissipation. It provides an intuitive explanation of the conditions necessary for optimal proofreading and reveals the unexpected capability of allosteric molecules to beat the Hopfield limit of fidelity by leveraging the diversity of states available to them. The framework that we have built for the piston model can also serve as a basis for additional studies of driven biochemical systems.