No f1 car doesn't have to have rear wing. Reason why BAR was illegal F1 car was because the rudder is moveable aero device, and mad is not allowed in f1.
are you blind? -no, I'm deaf, can't you see? -no, I'm blind.
the rudder was needed because it was a safety device. However, as legal as it may be, lopping off the rear wing for the speed run means it just isn't an F1 car anymore. Nobody is bothered about the rudder as it was needed to keep the car stable, however the removal of the rear wing undone the point in it as it's no longer an F1 cars top speed.