Like everthing else, there's a bit of tradeoff (airfoils have lift AND drag, don't you know).
But to merely call the stators "swirl-compensating" misses the point. They convert the swirl or vortex energy (which would otherwise be wasted in the slipstream) into increased static pressure
Precisely.
They take the swirl downstream of a (shrouded) fan, and convert it into (nonswirling, more direct) jet blast. They spend some of the energy for drag, but they still gain more energy by converting swirly slipstream to direct than they lose to drag.
Why cannot open propellers also install open stators behind the propeller? Converting swirl to more direct slipstream?