Recently, there has been growing interest in electrolysis under forced periodic dynamic conditions, known as pulsed electrolysis, due to its potential to enhance cell efficiency. In the context of water electrolysis, there is ongoing debate about whether pulsed electrolysis, which involves a superposition of direct current (DC) and alternating current (AC), can improve the efficiency compared to the steady-state (DC) operation. Some studies suggest that pulsed electrolysis enhances process efficiency while others report a decline. Here, we present a compelling argument that pulsed electrolysis consistently deteriorates the efficiency of water electrolysis. A proof using Jensen's inequality demonstrates that enhancing efficiency under pulsed electrolysis is impossible. The proof employs a common model describing the PEM electrolysis cell. Our findings conclude that steady-state (DC) operation is the optimal operating strategy to minimize specific power consumption and thus maximize the efficiency of water electrolyzers. We expect similar results for other electrolyzer models.