Frequency restoration in power systems is conventionally performed by broadcasting a centralized signal to local controllers. As a result of energy transition, technological advances, and scientific interest in distributed control and optimization methods, a plethora of distributed frequency control strategies have been proposed recently, which rely on communication amongst local controllers. In this paper, we propose a fully decentralized leaky integral controller for frequency restoration, which is derived from a classic lag element. We study steady-state, asymptotic optimality, nominal stability, input-to-state stability, noise rejection, transient performance, and robustness properties of this controller in closed loop with a nonlinear and multivariable power system model. We demonstrate that the leaky integral controller can strike an acceptable tradeoff between performance and robustness as well as between asymptotic disturbance rejection and transient convergence rate by tuning its dc gain and time constant. We compare our findings to conventional decentralized integral control and distributed-averaging-based integral control in theory and simulations.