We numerically investigate the attribute of omnidirectionality of the flow-control system comprised of a large circular cylinder equipped with eight spinning rods of smaller diameter, subject to an incoming flow that adopts different angles of attack. Detached-eddy simulations are employed to compute hydrodynamic loads and to provide flow topology at a Reynolds number of 1000. Two cases are assessed regarding the rods angular velocities. In case 0, all rods spun with the same angular velocity. In case 1, velocities were inspired by potential-flow theory. The two systems have the same input kinetic energy in common. To assess the system response, the velocities were increased proportionally. Both cases succeeded in reducing the mean drag. However, while case 1 proved to become ever “more omnidirectional” with increasing angular velocities, case 0 demonstrated to be prone to the angle of attack as it was unable to suppress vortex shedding for sufficiently large slopes of the incoming flow, and in such circumstances, unable to reduce hydrodynamic forces. We verify that the lift is mitigated in case 1, in contrast to case 0. Even for a vortex-free downstream flow resulting from configurations of high velocities and high angle of attack, the latter produces asymmetric recirculation regions downstream of the system that drive a pressure imbalance. The different outcomes of the two systems are also explored from the viewpoint of power consumption, and it is revealed that the omnidirectionality of case 1 is intrinsically related to the emphasis imposed on rotation rates of a subset of the eight rods.