We explore the averaged fusion reactivity of the reaction in tabletop laser experiments using a plasma expansion model. We investigate the energy distribution of proton beams accelerated by lasers as a function of electron temperature Te, characterizing the sheath field generated by fast electrons at the rear side of a laser-irradiated thin foil (pitcher target), and the dimensionless acceleration time , where ωpi is the ion plasma frequency. By combining these distributions with the fusion cross-section, we identify the optimal conditions that maximize the fusion reactivity, with at and . These findings suggest that an upper limit exists for the fusion reactivity achievable in laser-driven fusion experiments.