Robotic systems are increasingly relying on distributed feedback controllers to tackle complex and latency-prone sensing and decision problems. These demands come at the cost of a growing computational burden and, as a result, larger controller latencies. To maximize robustness to mechanical disturbances and achieve high control performance, we emphasize the necessity for executing damping feedback in close proximity to the control plant while allocating stiffness feedback in a latency-prone centralized control process. Additionally, series elastic actuators (SEAs) are becoming prevalent in torque-controlled robots during recent years to achieve compliant interactions with environments and humans. However, designing optimal impedance controllers and characterizing impedance performance for SEAs with time delays and filtering are still under-explored problems. The presented study addresses the optimal controller design problem by devising a critically-damped gain design method for a class of SEA cascaded control architectures, which is composed of outer-impedance and inner-torque feedback loops. Via the proposed controller design criterion, we adopt frequency-domain methods to thoroughly analyze the effects of time delays, filtering and load inertia on SEA impedance performance. These results are further validated through the analysis, simulation, and experimental testing on high-performance actuators and on an omnidirectional mobile base.